Questions tagged [quantum-mechanics]

Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.

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153
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11answers
67k views

Why don't electrons crash into the nuclei they “orbit”?

I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course. In particular, I can't see how a negatively charged electron can stay ...
86
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8answers
27k views

What is $\Delta t$ in the time-energy uncertainty principle?

In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to ...
112
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7answers
21k views

A list of inconveniences between quantum mechanics and (general) relativity?

It is well known that quantum mechanics and (general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them? E.g. relativity ...
70
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8answers
10k views

What really causes light/photons to appear slower in media?

I know that if we solve the Maxwell equation, we will end up with the phase velocity of light being related to the permeability and the permittivity of the material. But this is not what I'm ...
56
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10answers
11k views

Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. However, I wonder, is this actually a duality? At the most fundamental level, we 'know' ...
76
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5answers
14k views

What is spin as it relates to subatomic particles?

I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does ...
92
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7answers
45k views

Is the universe fundamentally deterministic?

I'm not sure if this is the right place to ask this question. I realise that this maybe a borderline philosophical question at this point in time, therefore feel free to close this question if you ...
91
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8answers
17k views

Why is quantum entanglement considered to be an active link between particles?

From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every ...
83
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17answers
144k views

What is a good introductory book on quantum mechanics?

I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for ...
26
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4answers
4k views

Validity of naively computing the de Broglie wavelength of a macroscopic object

Many introductory quantum mechanics textbooks include simple exercises on computing the de Broglie wavelength of macroscopic objects, often contrasting the results with that of a proton, etc. For ...
67
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5answers
10k views

What is more fundamental, fields or particles?

My confusion about quantum theory is twofold: I lack an adequate understanding of how the mathematics of quantum theory is supposed to correspond to phenomena in the physical world I still have an ...
33
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7answers
5k views

Isn't the uncertainty principle just non-fundamental limitations in our current technology that could be removed in a more advanced civilization?

From what I understand, the uncertainty principle states that there is a fundamental natural limit to how accurately we can measure velocity and momentum at the same time. It's not a limit on ...
77
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15answers
10k views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
47
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4answers
27k views

Why do electrons occupy the space around nuclei, and not collide with them?

We all learn in grade school that electrons are negatively-charged particles that inhabit the space around the nucleus of an atom, that protons are positively-charged and are embedded within the ...
78
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14answers
29k views

About the complex nature of the wave function?

1. Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
30
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5answers
2k views

Reason for the discreteness arising in quantum mechanics?

What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
78
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12answers
19k views

QM without complex numbers

I am trying to understand how complex numbers made their way into QM. Can we have a theory of the same physics without complex numbers? If so, is the theory using complex numbers easier?
66
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14answers
9k views

Why can't $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator?

In the time-dependent Schrodinger equation, $ H\Psi = i\hbar\frac{\partial}{\partial t}\Psi,$ the Hamiltonian operator is given by $$\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V.$$ Why can't we ...
31
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2answers
4k views

Rigged Hilbert space and QM

Are there any comprehensive texts that discuss QM using the notion of rigged Hilbert spaces? It would be nice if there were a text that went through the standard QM examples using this structure.
33
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7answers
11k views

What is an observer in quantum mechanics?

My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts. What is an observer? What are the conditions required to be qualified of observer, ...
20
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2answers
3k views

What does the Canonical Commutation Relation (CCR) tell me about the overlap between Position and Momentum bases?

I'm curious whether I can find the overlap $\langle q | p \rangle$ knowing only the following: $|q\rangle$ is an eigenvector of an operator $Q$ with eigenvalue $q$. $|p\rangle$ is an eigenvector of ...
46
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7answers
3k views

In quantum mechanics, given certain energy spectrum can one generate the corresponding potential?

A typical problem in quantum mechanics is to calculate the spectrum that corresponds to a given potential. Is there a one to one correspondence between the potential and its spectrum? If the answer ...
18
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1answer
2k views

The choice of measurement basis on one half of an entangled state affects the other half. Can this be used to communicate faster than light?

It is often stated, particularly in popular physics articles and videos, that if one measures a particle A that is entangled with some other particle B, then this measurement will immediately affect ...
52
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1answer
3k views

Why exactly do sometimes universal covers, and sometimes central extensions feature in the application of a symmetry group to quantum physics?

There seem to be two different things one must consider when representing a symmetry group in quantum mechanics: The universal cover: For instance, when representing the rotation group $\mathrm{SO}(3)...
87
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10answers
12k views

Quantum Entanglement - What's the big deal?

Bearing in mind I am a layman - with no background in physics - please could someone explain what the "big deal" is with quantum entanglement? I used to think I understood it - that 2 particles, say ...
15
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3answers
4k views

Smoothness constraint of wave function

Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't ...
40
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4answers
3k views

Hilbert space of harmonic oscillator: Countable vs uncountable?

Hm, this just occurred to me while answering another question: If I write the Hamiltonian for a harmonic oscillator as $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$ then wouldn't one set of ...
27
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3answers
7k views

Time as a Hermitian operator in quantum mechanics

In non-relativistic QM, on one hand we have the following relations: $$\langle x | P | \psi \rangle ~=~ -i \hbar \frac{\partial}{\partial x} \psi(x),$$ $$\langle p | X | \psi \rangle ~=~ i \hbar \...
21
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3answers
6k views

How can we interpret polarization and frequency when we are dealing with one single photon?

If polarization is interpreted as a pattern/direction of the electric-field in an electromagnetic wave and the frequency as the frequency of oscillation, how can we interpret polarization and ...
99
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10answers
11k views

Is Angular Momentum truly fundamental?

This may seem like a slightly trite question, but it is one that has long intrigued me. Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and ...
45
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5answers
20k views

What is the connection between Poisson brackets and commutators?

The Poisson bracket is defined as: $$\{f,g\} ~:=~ \sum_{i=1}^{N} \left[ \frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} - \frac{\partial f}{\partial p_{i}} \frac{\partial g}{\...
61
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8answers
5k views

Why is the application of probability in QM fundamentally different from application of probability in other areas?

Why is the application of probability in quantum mechanics (QM) fundamentally different from its application in other areas? QM applies probability according to the same probability axioms as in other ...
9
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1answer
3k views

Why path integral approach may suffer from operator ordering problem?

In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path. What did ...
10
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6answers
2k views

Does a photon instantaneously gain $c$ speed when emitted from an electron?

An excited electron looses energy in the form of radiations. The radiation constitutes photons which move at a speed $c$. But, is the process of conversion of the energy of the electron into the ...
11
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2answers
2k views

Are all scattering states un-normalizable?

I am an undergraduate studying quantum physics with the book of Griffiths. in 1-D problems, it said a free particle has un-normalizable states but normalizable states can be obtained by sum up the ...
17
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2answers
6k views

Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate?

The standard treatment of the one-dimensional quantum simple harmonic oscillator (SHO) using the raising and lowering operators arrives at the countable basis of eigenstates $\{\vert n \rangle\}_{n = ...
25
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4answers
3k views

$\lambda=\frac{2h}{p}$ instead of $\lambda=\frac{h}{p}$?

I am studying quantum physics and there is something I don't understand: I know that for any particle $E=hf$ (Einstein relation) and $v=\lambda f$ ($v$ is the speed of the particle). I also know ...
49
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9answers
10k views

Can the photoelectric effect be explained without photons?

Lamb 1969 states, A misconception which most physicists acquire in their formative years is that the photoelectric effect requires the quantization of the electromagnetic field for its explanation. ...
35
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5answers
4k views

Is there oscillating charge in a hydrogen atom?

In another post, I claimed that there was obviously an oscillating charge in a hydrogen atom when you took the superposition of a 1s and a 2p state. One of the respected members of this community (...
23
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3answers
22k views

Don't understand the integral over the square of the Dirac delta function

In Griffiths' Intro to QM [1] he gives the eigenfunctions of the Hermitian operator $\hat{x}=x$ as being $$g_{\lambda}\left(x\right)~=~B_{\lambda}\delta\left(x-\lambda\right)$$ (cf. last formula on ...
11
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5answers
6k views

How does the momentum operator act on state kets?

I have been going through some problems in Sakurai's Modern QM and at one point have to calculate $\langle \alpha|\hat{p}|\alpha\rangle$ where all we know about the state $|\alpha\rangle$ is that $$\...
5
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3answers
2k views

Normalization of basis vectors with a continuous index?

I have an infinite basis which associates with each point, $x$, on the $x$-axis, a basis vector $|x\rangle$ such that the matrix of $|x\rangle$ is full of zeroes and a one by the $x^{\mathrm{th}}$ ...
2
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1answer
3k views

Time-independent Schrödinger function: If the potential $V$ is even, then the wave function $\psi$ can always be taken to be either even or odd

I have done the Problem 2.1 in Griffiths' quantum mechanics, and it seems not making sense to me. What if the wave function isn't symmetric at all? Then obviously the proof doesn't work. The ...
14
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1answer
2k views

Schrödinger wavefunctional quantum-field eigenstates

The reason that I have this problem is that I'm trying to solve problem 14.4 of Schwartz's QFT book, which've confused me for a long time. The problem is to construct the eigenstates of a quantum ...
19
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6answers
4k views

How do we know that entanglement allows measurement to instantly change the other particle's state? [duplicate]

I have never found experimental evidence that measuring one entangled particle causes the state of the other entangled particle to change, rather than just being revealed. Using the spin up spin down ...
18
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6answers
4k views

Is it possible to recover Classical Mechanics from Schrödinger's equation?

Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the ...
11
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2answers
3k views

Why are eigenfunctions which correspond to discrete/continuous eigenvalue spectra guaranteed to be normalizable/non-normalizable?

These facts are taken for granted in a QM text I read. The purportedly guaranteed non-normalizability of eigenfunctions which correspond to a continuous eigenvalue spectrum is only partly justified by ...
15
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3answers
985 views

What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$?

I've read that plane wave equations can be represented in various forms, like sine or cosine curves, etc. What is the part of the imaginary unit $i$ when plane waves are represented in the form $$f(x) ...
58
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9answers
5k views

Is the uncertainty principle a property of elementary particles or a result of our measurement tools?

In many physics divulgation books I've read, this seems to be a commonly accepted point of view (I'm making this quote up, as I don't remember the exact words, but this should give you an idea): ...
44
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9answers
23k views

What equation describes the wavefunction of a single photon?

The Schrödinger equation describes the quantum mechanics of a single massive non-relativistic particle. The Dirac equation governs a single massive relativistic spin-½ particle. The photon is a ...