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 ...

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Should it be obvious that independent quantum states are composed by taking the tensor product?

My text introduces multi-quibt quantum states with the example of a state that can be "factored" into two (non-entangled) substates. It then goes on to suggest that it should be obvious1 that the ...
9
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4answers
1k views

What does a de Broglie wave look like?

What does a de Broglie wave look like? Are de Broglie waves transverse or longitudinal? Can they be polarized? What about the de Broglie wave of a ground state neutral spin-zero Helium 4 atom? ...
7
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1answer
441 views

Hilbert space of a free particle: Countable or Uncountable?

This is obviously a follow on question to the Phys.SE post Hilbert space of harmonic oscillator: Countable vs uncountable? So I thought that the Hilbert space of a bound electron is countable, but ...
5
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1answer
459 views

Time-ordering vs normal-ordering and the two-point function/propagator

I don't understand how to calculate this generalized two-point function or propagator, used in some advanced topics in quantum field theory, a normal ordered product (denoted between $::$) is ...
9
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6answers
1k views

Will Determinism be ever possible?

What are the main problems that we need to solve to prove Laplace's determinism correct and overcome the Uncertainty principle?
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5answers
1k views

Does entanglement not immediately contradict the theory of special relativity?

Does entanglement not immediately contradict the theory of special relativity? Why are people still so convinced nothing can travel faster than light when we are perfectly aware of something that ...
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2answers
4k views

Speed of a particle in quantum mechanics: phase velocity vs. group velocity

Given that one usually defines two different velocities for a wave, these being the phase velocity and the group velocity, I was asking their meaning for the associated particle in quantum mechanics. ...
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4answers
2k views

How to tackle 'dot' product for spin matrices

I read a textbook today on quantum mechanics regarding the Pauli spin matrices for two particles, it gives the Hamiltonian as $$ H = \alpha[\sigma_z^1 + \sigma_z^2] + ...
8
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1answer
680 views

exponential potential $ \exp(|x|) $

For $a$ being positive what are the quantisation conditions for an exponential potential? $$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$ with boundary conditions $$ y(0)=0=y(\infty) $$ I ...
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6answers
3k views

Linear Algebra for Quantum Physics

A week ago I asked people on this forum what mathematical background was needed for understanding Quantum Physics, and most of you mentioned Linear Algebra, so I decided to conduct a self-study of ...
2
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2answers
990 views

EPR-type experiments and faster-than-light communication using interference effects as signaling mechanism

I understand that faster-than-light communication is impossible when making single measurements, because the outcome of each measurement is random. However, shouldn't measurement on one side collapse ...
6
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1answer
2k views

Momentum as Generator of Translations

I understand from some studies in mathematics, that the generator of translations is given by the operator $\frac{d}{dx}$. Similarly, I know from quantum mechanics that the momentum operator is ...
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5answers
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How can the nucleus of an atom be in an excited state?

An example of the nucleus of an atom being in an excited state is the Hoyle State, which was a theory devised by the Astronomer Fred Hoyle to help describe the vast quantities of carbon-12 present in ...
2
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1answer
147 views

Two-Person Problem

The following is a thought experiment I've been stuck on. (No, this isn't homework. I made it up.) Here it is: Two-Person Problem Let's say we have a superposed particle going through a tube. ...
2
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5answers
413 views

Wave/particle duality

Apologies if this has been asked before (I did check and I believe it wasn't). I have a question about the particle/wave duality of photons (or other particles). Depending on what and how we measure ...
-1
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1answer
359 views

confusion on quantum field theory [closed]

Having read Art Hobsons paper on Quantum field theory, he states " the field collapses into a field of atomic size" This seems to be stating that each field quanta is a different quantum field? Like 2 ...
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2answers
237 views

How exactly does applying the Equipartition Theorem to radiation leads to UV catastrophe?

I'm reading a book by George Gamow, "Thirty years that shook Physics" and have trouble understanding his way of describing the UV catastrophe. In a first part he points out that applying the ...
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10answers
3k views

What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
20
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3answers
3k views

What's wrong with this derivation that $i\hbar = 0$?

Let $\hat{x} = x$ and $\hat{p} = -i \hbar \frac {\partial} {\partial x}$ be the position and momentum operators, respectively, and $|\psi_p\rangle$ be the eigenfunction of $\hat{p}$ and therefore ...
29
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3answers
15k views

Maximum theoretical data density

Our ability to store data on or in physical media continues to grow, with the maximum amount a data you can store in a given volume increasing exponentially from year to year. Storage devices continue ...
21
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7answers
3k views

Is (rest) mass quantized?

I learned today in class that photons and light are quantized. I also remember that electric charge is quantized as well. I was thinking about these implications, and I was wondering if (rest) mass ...
9
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3answers
944 views

How does one determine ladder operators systematically?

In textbooks, the ladder operators are always defined," and shown to 'raise' the state of a system, but they are never actually derived. Does one find them simply by trial and error? Or is there a ...
19
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10answers
11k views

Does the Pauli exclusion principle instantaneously affect distant electrons?

According to Brian Cox in his A night with the Stars lecture$^1$, the Pauli exclusion principle means that no electron in the universe can have the same energy state as any other electron in the ...
12
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3answers
674 views

Why does spin have a discrete spectrum?

Why is it that unlike other quantum properties such as momentum and velocity, which usually are given through (probabilistic) continuous values, spin has a (probabilistic) discrete spectrum?
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2answers
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How does quantum trapping with diamagnets work?

I just saw this demonstration by someone from a Tel Aviv University lab. What they achieved there is mind blowing. I myself own a levitron that uses the Hall effect to levitate a magnet, the problem ...
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4answers
1k views

Can Planck's constant be derived from Maxwell's equations?

Can mathematics (including statistics, dynamical systems,...) combined with classical electromagnetism (using only the constants appearing in chargefree Maxwell equations) be used to derive the Planck ...
14
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1answer
646 views

What is the conclusion from Aharonov-Bohm Effect?

What is the conclusion that we can draw from the Aharonov-Bohm effect? Does it simply suggest that the vector potential has measurable effects? Does it mean that it is a real observable in quantum ...
14
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2answers
814 views

What Hermitian operators can be observables?

We can construct a Hermitian operator $O$ in the following general way: find a complete set of projectors $P_\lambda$ which commute, assign to each projector a unique real number $\lambda\in\mathbb ...
8
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2answers
5k views

How does electron move around nucleus?

I need to get a nice picture about how electron moves around nucleus? I find concept of probability and orbitals quite difficult to understand?
8
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4answers
5k views

Is Dr Quantum's Double Slit Experiment video scientifically accurate?

I'm fascinated by the fundamental questions raised by the Double Slit Experiment at the quantum level. I found this "Dr Quantum" video clip which seems like a great explanation. But is it ...
7
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3answers
1k views

What is quantum entanglement?

What is quantum entanglement? Please be pedagogical. Edit: I have updated my background under my profile.
6
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2answers
1k views

Weyl Ordering Rule

While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian ...
6
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1answer
456 views

Quantum Zeno effect and unstable particles

Is it possible to increase indefinitely the lifetime of unstable particles by applying the quantum Zeno effect? Is there a bound from theoretical principles about the maximum extension one can get in ...
3
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5answers
761 views

Commutator algebra in exponents

Considering $X$ and $Y$ such that $[X,Y]=\lambda$, which is complex, and $\mu$ is another complex number, prove: $$e^{\mu(X+Y)}=e^{\mu X} e^{\mu Y} e^{-\mu^2\lambda/2}$$ My attempt (so far) is: ...
10
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1answer
1k views

3D Delta Potential Well

The 1D delta potential well $V(x) = -A\delta(x - a)$ always has exactly one bound state. The same is true for the 3D delta potential well $V(\vec{r}) = -A\delta(\vec{r}-\vec{a})$. I can show this for ...
9
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4answers
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Electrons - What is Waving?

If an electron is a wave, what is waving? So many answers on the internet say "the probability that a particle will be at a particular location"... so... the electron is a physical manifestation of ...
8
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4answers
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Study Quantum Physics

I'm an aspiring physicist who wants to self study some Quantum Physics. My thirst for knowledge is unquenchable and I can not wait 2 more years until I get my first quantum physics class in ...
6
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4answers
542 views

Is uncertainty principle a technical difficulty in measurement?

Is the uncertainty principle a technical difficulty in measurement or is it an intrinsic concept in quantum mechanics irrelevant of any measurement? Everyone knows the thought experiment of measuring ...
5
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1answer
561 views

Why is the value of spin +/- 1/2?

I understand how spin is defined in analogy with orbital angular momentum. But why must electron spin have magnetic quantum numbers $m_s=\pm \frac{1}{2}$ ? Sure, it has to have two values in ...
4
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4answers
837 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 ...
8
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2answers
25k views

What is in the space between a nucleus of an atom and its electrons?

There is a common analogy about the structure of an atom, such as the nucleus is a fly in the centre of a sports stadium and the electrons are tiny tiny gnats circling the stadium (tip of the hat to ...
7
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4answers
925 views

Why the statement “there exist at least one bound state for negative potential” doesn't hold for 3D case?

Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal. However, today I'm doing a homework considering a potential like ...
5
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3answers
897 views

Didn't we mess up with the temperature?

The following passage has been extracted from the book "The Feynman Lectures on Physics-Vol l": The mean kinetic energy is a property only of the "temperature." Being a property of the ...
3
votes
2answers
189 views

Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
3
votes
3answers
2k views

Matrix elements of momentum operator in position representation

I have two related questions on the representation of the momentum operator in the position basis. The action of the momentum operator on a wave function is to derive it: $$\hat{p} ...
7
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5answers
616 views

How isolated must a system be for it's wave function to be considered not collapsed?

As an undergrad I was often confused over people's bafflement with Schodinger's cat thought experiment. It seemed obvious to me that the term "observation" referred to the Geiger counter, not the ...
5
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2answers
2k views

Conservation of Energy in a magnet

When a permanent magnet attracts some object, lets say a steel ball, energy is converted into for instance kinetic energy and heat when attraction happens, and they eventually collide. Does this imply ...
4
votes
5answers
6k views

Is it possible to transfer classical bits of information faster than light speed?

Is there any known, verifiable way to transfer classical information faster than light, using quantum entanglement or other phenomenon? Does quantum teleportation, or other known phenomenon, allow ...
3
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3answers
1k views

Can we have discontinuous wavefunctions in the Infinite Square well?

The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
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0answers
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Do particles travel backward and forward in time? [duplicate]

All these classical ideas are pointless and obsolete today, because in quantum mechanics, the particles are completely different objects, defined by quantum motion of fields, not by the location of ...