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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365 views

What is the fundamental differences between bound and entangled states

Specifically, are all entangled states considered bound?
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1answer
1k views

why is total electron energy of an electron in metal negative?

In my textbook, it says that any electron bound in metals, modelled as some potential well $U$, has negative total electron energy, as shown below in the figure. Why is the total electron energy ...
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4answers
2k views

What is happening over the 15 minutes it takes a neutron to decay?

I've read that free neutrons decay into a proton, electron and neutrino with an average lifespan of about 15 minutes. Is there anything physically different about a neutron that has existed for 14 ...
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1answer
2k views

What does the concept of phase space mean in particle physics?

I came across the concept of phase space in statistical mechanics. How does this concept come about in particle physics? Why was it introduced and how is it used? What does it mean when ...
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2answers
134 views

Time-dependence in LCAO

I would like to study time-dependence (TD) in linear combinations of atomic orbitals (LCAO). The Hückel method enables quick and dirty determination of MOs for suitable systems (view link for ...
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1answer
710 views

wavefunction collapse and uncertainty principle

We all know that wavefunction collapse when it is observed. Uncertainty principle states that $\sigma_x \sigma_p \geq \frac {\hbar}{2}$. When wavefunction collapse, doesn't $\sigma_x$ become $0$?, as ...
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1answer
851 views

Quantum mechanic newbie: why complex amplitudes, why Hilbert space? [duplicate]

I'm just starting learning quantum mechanics by myself (2 "lectures" so far) and I was wondering why we need to define quantum states in a complex vector space rater than a real one? Also I was ...
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4answers
181 views

The notion of bounded states in quantum mechanics and their characterization with operators

Is there any case of potential $V$, such that the continuity of the operator $H=c\ \Delta+V$ is not spoiled? And I don't know any non-differnetial operator examples for continous spectra. I ...
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3answers
762 views

Existence of creation and annihilation operators

In a multiple particle Hilbert space (any space of any multi-particle system), is it sufficient to define creation and annihilation operators by their action (e.g. mapping an n-particle state to an ...
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1answer
427 views

Why and how is nondegenerate perturbation theory used for time evolution under $\vec{L}.\vec{S}$ coupling?

Let us say that we start with an electron which is in a spin up state and has a spatial wave-function of the form $xf(r)$. Then one turns on a perturbation of the form ...
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1answer
109 views

How to take the limit from 3D to 1 D in quantum mechanics?

Take a particle of mass $m$ trapped in an infinite potential well between $0$ and $a$. The energy spectrum and the wave functions are $$\displaystyle E_n = \frac{\hbar^2\pi^2}{2ma^2} n^2$$ ...
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0answers
171 views

direct conversion of heat to electric potential / current - are there theories that contradict the 'Kelvin Statement'?

In particular, William Thomson (Kelvin) appeared to be wrong about key things in physics (initially X-rays, aether, even aviation feasibility). ...
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5answers
4k views

Is quantum entanglement functionally equivalent to a measurement?

I saw the following talk the other day: http://www.youtube.com/watch?v=dEaecUuEqfc&feature=share In it, Dr. Ron Garret posits that entanglement isn't really that "special" of a property. He ...
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2answers
1k views

Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon?

Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon? If so, can quantum mechanics describe the universe at high energies where there is no ...
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0answers
144 views

Non-Locality and Entanglement

Let’s consider a pair of particles [with their signals] comprising an isolated system. Any change in some property of either particle is due to the signal/s received from the other. Each particle has ...
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2answers
310 views

Was Planck's constant $h$ the same when the Big Bang happened as it is today?

Was Planck's constant $h$ the same when the Big Bang happened as it is today? Planck's constant : $$h= 6.626068 × 10^{-34}\, m^2 kg / s,$$ $$E=n.h.\nu,$$ $$\epsilon=h.\nu$$
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5answers
425 views

wave superposition of electrons and quarks

Is quantum wave superposition of electrons and quarks possible? If not, can different types of elementary particles be mixed in wave superposition?
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1answer
2k views

Is the universe linear? If so, why?

Simple question, I'm trying to build a quantum memory system that utilizes the superposition principle to model specific phenomenon I am trying to predict, anyways, my question is this. Is the ...
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5answers
2k views

What do we actually mean when we say that matter is a wave?

What do we actually mean when we say that matter is a wave? What does the wavelength of this matter wave indicate? The idea of a particle behaving like a wave is kinda incomprehensible to me. ...
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2answers
2k views

Matrix Representations of Quantum States and Hamiltonians

I am a high school student trying to teach himself quantum mechanics just for fun, and I am a bit confused. As a fun test of my programming/quantum mechanics skill, I decided to create a computer ...
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1answer
146 views

Matter wave of multiple particles of different types

I am slightly getting confused on the following issue: When performing double-slit experiment of electrons, a screen allows the matter waves to be detected as particles. And as we all know that ...
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1answer
319 views

How do you determine the degree of localization of a wavefunction?

Suppose that there is a wavefunction $\Psi (x,0)$ where 0 is referring to $t$. Let us also say that $a(k) = \frac{C\alpha}{\sqrt{\pi}}\exp(-\alpha^2k^2)$ is the spectral contents (spectral amplitudes) ...
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3answers
494 views

What is the physical meaning of weak expectation values?

In the two-state formalism of Yakir Aharonov, the weak expectation value of an operator $A$ is $\frac{\langle \chi | A | \psi \rangle}{\langle \chi | \psi \rangle}$. This can have bizarre properties. ...
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2answers
2k views

Bohr model with all Quantum numbers for hydrogen atom

bohr model: $$E_n=-\frac {\mathcal R}{n^2(1+\frac {m_e}{m_p})}$$ can we developed bohr model with all Quantum Numbers of the Hydrogen Atom? $R(r)$ Principal quantum number $$n=1,2,3,4,5,...,n$$ ...
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1answer
530 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 ...
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2answers
171 views

From what we know about QM and Elements could we simulate the Universe in a Computer?

From what we know now about Quantum Mechanics and Elements, could we simulate life the Universe at a Quantum to Element level? If we can't assume enough to create a sim, what fundamentals are we ...
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15answers
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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 ...
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1answer
3k views

Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view: Anomalies are due to the fact that quantum field ...
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2answers
747 views

Why is $\Delta x \Delta k \approx 1$ in any pulse?

In my physics textbook, it says that for any pulse, if $\Delta x$ becomes smaller, $\Delta k$ becomes larger where $k$ refers to $2\pi/\lambda$ and $x$ is x-axis displacement, as described by $\Delta ...
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2answers
782 views

Examples of discrete Hamiltonians?

I have a strong interest in the mathematical structure of quantum mechanics. I'm particularly interested in discrete systems, i.e. systems whose state is in a finite-dimensional Hilbert space. Up to ...
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3answers
1k views

What is a completely positive map *physically*?

I am sure this question is really stupid, but I could not refrain from asking it in this forum. This can be considered as a continuation of this question. ...
2
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1answer
125 views

How are quantum phenomena in atoms and molecules protected against decoherence?

It became widely accepted that quantum effects don't show up in macroscopic objects due to the process of decoherence, in which the interaction with the enormous number of degrees of freedom of the ...
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2answers
221 views

Multiplicity of eigenvalues of angular momentum

Reading Dirac's Principles of Quantum Mechanics, I encounter in § 36 (Properties of angular momentum) this fragment: This is for a dynamical system with two angular momenta $\mathbf{m}_1$ and ...
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2answers
6k views

Why Silver atoms were used in Stern-Gerlach experiment?

For the Stern-Gerlach experiment done in 1922: Why were silver atoms used? Silver atoms contain many electrons in different shells (with different angular momemtum quantum numbers. Why are those not ...
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1answer
54 views

In which way is decoherence not symmetric between the two considered systems?

If a quantum system interacts with a "big" quantum system, you have dephasing. The models of decoherence all have this atog aproach to them, about what is to understood of the interaction of the ...
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4answers
233 views

What counts as an observer and memory states in quantum interpretations?

The Everett interpretation has memory robots. Copenhagen requires observer memory states. Consistent histories has its IGUSes. Decoherence has its existential interpretation. All of them refer to ...
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3answers
466 views

A nonintegrable quantum system whose classical limit is integrable?

In this discussion: http://chat.stackexchange.com/rooms/4243/discussion-between-arnold-neumaier-and-ron-maimon Arnold Neumaier suggested that there might be a close link between classical and quantum ...
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1answer
316 views

How are quantum potential wells fabricated?

Potential wells, such as infinite and finite potential well, have been the standard examples in quantum mechanics textbooks for tens of years. They started being only theoretical toy models but as ...
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2answers
3k views

Can I study Quantum Computing or Quantum Mechanics with an Engineering background?

I am currently studying Electrical & Electronic Engineering. I wish to pursue Quantum Mechanics or Quantum Computing as my research subject. Is it possible for me to do my M.Tech. and then pursue ...
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8answers
6k views

Is it theoretically possible to reach 0 kelvin?

I'm having a discussion with someone. I said that it is -even theoretically- impossible to reach 0K, because that would imply that all molecules in the substance would stand perfectly still. He said ...
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1answer
785 views

How do I solve these integrals of wave function and operator?

First integral $$\int \Psi^*({\bf r},t)\hat {\bf p} \Psi({\bf r},t)\, d^3r,$$ where the $\Psi({\bf r},t)=e^{i({\bf k}\cdot{\bf r}-\omega t)}\,\,\,$ and $\hat {\bf p}=-i\hbar \nabla$. Second one ...
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1answer
389 views

Conjugate Transpose of Hamiltonian Matrix

I read some notes saying, $$i\hbar \frac{dC_{i}(t)}{dt} = \sum_{j}^{} H_{ij}(t)C_{j}(t)\tag{1}$$ where $C_{i}(t) = \langle i|\psi(t)\rangle$ and $H_{ij}$ is hamiltonian matrix. However, what is ...
7
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2answers
202 views

Under what assumptions can we split a Hilbert space into subspaces?

I was thinking about an apparently simple question about quantum mechanics, if I am looking at a quantum system described by a Hilbert space $\cal{H}$ under what hypothesis can I define A and B as ...
2
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3answers
313 views

How to observe a particle with indefinite position?

As I understand it, when physicists talk about something behaving both like a particle and a wave, what they mean is that it has momentum like a particle, but its position is determined ...
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0answers
97 views

After quantization of electron vibrations, do we need electrons anyway?

The title question is not ment in a general context, but one in which goes to the plasmon theory. In that case, how is are the statistics (boson vs. fermions) of plasmons determined? And is there an ...
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5answers
3k views

Why position is not quantized in quantum mechanics?

Usually in all the standard examples in quantum mechanics textbooks the spectrum of the position operator is continuous. Are there (nontrivial) examples where position is quantized? or position ...
6
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2answers
666 views

Is temperature quantized?

I'm learning quantum mechanics on my own. I've known that energy is quantized and I've started wondering about temperature. From thermodynamics we have: $$U=\frac{3}{2}NkT $$ (for ideal gas, of ...
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4answers
559 views

particle accelerators and Heisenberg uncertainty principle

In accelerators we shoot very high momentum particles at each other to probe their structure at very small length scales. Has that anything to do with the HUP that addresses the spread of momentum and ...
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1answer
632 views

Historical: Natural vs unnatural parity mesons

Quick question: In the old papers and text I occasionally see authors referring to mesonic states as having 'natural parity' or 'unnatural parity'. What was their motivation for classifying mesons ...
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1answer
201 views

Question regarding the Bohm interpretation [closed]

I tried to understand the Bohm interpretation and this is what picture appeared to me. Please tell me if I understood something incorrectly. All particles have definite positions and follow ...