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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The status / acceptance of block time?

What is the current status or acceptance of block time as it relates to Einstein's theory of relativity? Has quantum mechanics ruled it out or is it still the favored view of the world? Perhaps there ...
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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} ...
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324 views

Why is the Wick contraction in HFB or BCS equal to a single-particle density?

I'm trying to understand how in Hartree-Fock-Bogoliubov (HFB) or BCS theory we can write a product of creation/annihilation operators as single-particle densities under the guise of "Wick's theorem". ...
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582 views

What is the mathematical background needed for quantum physics? [duplicate]

I'm a computer scientist with a huge interest in mathematics. I have also recently started to develop some interest about quantum mechanics and quantum field theory. Assuming some knowledge in the ...
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862 views

Minimal Kinetic energy for particle in a box

This is driving me crazy! The question goes as follows: A proton is enclosed in a zone of length 2pm along the x-axis. The minimal kinetic energy of the proton lies closest to: 5000eV 0.5eV 50eV ...
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How is multiplicity given by 2S+1?

Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}$, $l_1 = 1$ and $s_2 = \frac{1}{2}$, $l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either $+2$, $+1$ ...
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436 views

Born-Oppenheimer separation in Dirac bra-ket notation

Most derivations I have seen of the Born-Oppenheimer approximation are made using wave-functions. To understand it better, I was trying to write a derivation using Dirac notation, but I am stuck. I am ...
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925 views

When and how did the idea of the tensor product originate in the history quantum mechanics?

At some point in the history of quantum mechanics, it was accepted that a single particle is described by a wavefunction which is a function of the position of the particle $\mathbf{r}$, denoted: ...
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880 views

Can silicon droplets bouncing on a vibrating surface be a model for Quantum Mechanics?

In this video on youtube it is claimed that silicon droplets bouncing on a vibrating surface show behaviour in analogy to particle/wave duality in Quantum Mechanics. Is this true? Did they ...
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190 views

Born Oppenheimer Approximation: Why can any molecular state be represented as a linearcombination of electronic states?

in the Born Oppenehimer Approximation, one expands the molecular wavefunction $\Psi(x,X)$ in terms of the electronic wavefunctions $\phi(x;X)$: $\Psi(x,X)$ = $ \sum_k(c(X)_k\phi(x;X)_k)$ (x are the ...
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47 views

Why the peak of spectrum gets vague when the dimension is lower?

In a many-body system, we can know the spectrum function at a particular temperature from Green function. It means density of states. A peak of spectrum represents one mode. My question is that in the ...
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416 views

How can electrons be confined in Quantum dots?

Atoms are in the range of $1$ Angstrom while Quantum dots are in the range of $2$-$10$ nm. In any atom, $99.9$% is unoccupied. So if I have a Quantum dots of size $3$ nm and suppose in my Quantum dot, ...
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451 views

What are the “loopholes” in past Bell's theorem experiments?

I am intrigued by the following Phys.org article: Researchers began using photons in 1980s to test Bell's theory and determine if Einstein's reasoning is right or wrong. Since then, researchers ...
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348 views

Charged quantum particle in a magnetic field - choosing a different gauge leads to different wavefunctions

Consider a charged quantum particle confined to the $xy$ plane, subject to a magnetic field $\mathbf{B}=B\hat{z}$. The Hamiltonian is: $$ H = \frac{1}{2m} \left( \mathbf{p} - \frac{e ...
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1k views

Infinite square well in momentum space

As we know the eigenfunctions for a particle of mass m in an infinite square well defined by $V(x) = 0$ if $0 \leq x \leq a$ and $V(x) = \infty$ otherwise are: $\psi_n (x) = \sqrt{(2/a)} sin(n \pi ...
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3k views

Particle in infinite potential well which is doubled in size at $t_0$

I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding. The Problem: A Particle sits in an infinite potential well ...
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2answers
143 views

How should I simulate the electric potential field from a wavefunction?

I was interested in making what I thought would be a simple simulation of an electron encountering a positron by numerically solving the Schrodinger equation over several time steps, but I've run ...
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69 views

What exactly is the spin of a particle? [duplicate]

Possible Duplicate: What is spin as it relates to subatomic particles? I'm having a hard time grasping the concept of spin, my textbook describes it very vaguely: Stable matter contains ...
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1answer
565 views

Expectation values-Wavefunction

I'm a bit puzzled about an excercise in which I have to find the expectation values for position and momentum. Normally this should be pretty easy but in this case I just don't get the point. ...
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3answers
3k views

Partition function for quantum harmonic oscillator

Hi guys I'm currently trying to solve a mock exam for an exam in a few days and am a bit confused by the solutions they gave us for this exercise: Exercise: A solid is composed of N atoms which ...
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4answers
237 views

Could an ultra-relativistic particle tunnel directly through a stellar mass black hole?

It occurred to me in passing that the Lorentz contraction of a black hole from the perspective of an ultra-relativistic (Lorentz factor larger than about 10^16) particle could reduce the thickness of ...
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2answers
798 views

Constructing the exponential form of a unitary operator

I think I've got this figured out but wanted to make sure I'm doing this right. Working with operators that satisfy bosonic commutation relations $[b,b^\dagger] = 1$, I define a very general unitary ...
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1answer
867 views

Is the Pauli exclusion principle as Brian Cox described it? [duplicate]

Possible Duplicate: Does the Pauli exclusion principle instantaneously affect distant electrons? If this rule works, could you not set up an experiment to test the theory (as described by ...
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770 views

How do I find the eigenvalues for the angular momentum ladder operators?

I am trying to calculate the normalising constants for the angular momentum ladder operators but am stuck when I need to calculate expected values. How can I find the expected values
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140 views

What do the $j$ and $m$ stand for in $|j,m\rangle$ for angular momentum in quantum mechanics?

I'm assuming it is a jth state with m value as total angular momentum?
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3k views

Deriving group velocity

At the introduction to quantum mechanic phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get equation: $$ \scriptsize v_p=\frac{\omega}{k} $$ What i dont ...
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170 views

Scattering from a box potential of width $L$ doesn't reproduce a step potential in the limit $L \rightarrow \infty$

Consider the scattering of a quantum particle in one dimension, caused by a step in the potential (this appears in many undergrad level QM books): $$ V(x) = \begin{cases} V_1 & x<0 \\ V_2 ...
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757 views

Meaning of $\int \phi^\dagger \hat A \psi \:\mathrm dx$

While analysing a problem in quantum Mechanics, I realized that I don't fully understand the physical meanings of certain integrals. I have been interpreting: $\int \phi^\dagger \hat A \psi ...
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326 views

Question about Wigner's friend

The Wigner's friend thought experiment can be used to understand non-realism in quantum mechanics. For anyone not familiar, the thought experiment involves two researchers observing an experiment at ...
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1answer
268 views

How is energy transferred between atoms in a collision?

Consider two bare protons. One (A) is stationary (relative to some arbitrary massless observer); the other (B) is approaching A at 1 m/s. When they collide, I assume that they bounce. What is the ...
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2answers
396 views

Hydrogen atom in quantum mechanics

I have problems following the calculations in Griffiths' Introduction to Quantum Mechanics (Chapter 4.2.1): If you apply the Schrödinger equation to the Coulomb potential you get the following ...
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132 views

Is a large system just a set of smaller systems?

All particles exhibit wave-particle duality. And I have a strange question. Why does a larger system, liken an atom that is just a set of smaller systems, itself exhibit wave-particle duality? In ...
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325 views

Do scientists literally believe the Schröedinger's cat though experiment?

I've heard the Schrödinger's cat "paradox" (although there's nothing particularly paradoxical about it, just counterintuitive), but I've never been clear on whether or not it's meant to be taken with ...
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Physical Significance of Fourier Transform and Uncertainty Relationships

What is the physical significance of a fourier transform? I am interested in knowing exactly how it works when crossing over from momentum space to co ordinate space and also how we arrive at the ...
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884 views

Commutator with expontential [A, exp(B)]

How can I tell if $A$ and $\exp(B)$ commute? For $[A, B]$ it's simply $AB-BA$ and for $[\exp(A), \exp(B)]$ I think it'd be $\exp(A)\exp(B) - \exp(B)\exp(A) = \exp(A+B) - \exp(B+A) = 0$. Update: it's ...
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224 views

do quantum fields exist in superposition?

Wikipedia states in QFT all fields generally exist in superpostion. Is this correct? So my question is in quantum field theory, are the fields in quantum field theory existing persistently in ...
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414 views

Probability and probability amplitude

The equation: $$P = |A|^2$$ appears in many books and lectures, where $P$ is a "probability" and $A$ is an "amplitude" or "probability amplitude". What led physicists to believe that the square of ...
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483 views

Prove that the first order perturbation theory overestimates fundamental state [closed]

This was a question on my exam and I don't know how to solve it. Use the variational principle to prove that the first order perturbation theory always overestimates the energy of the fundamental ...
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2answers
2k views

Is Schrödinger’s cat misleading? And what would happen if Planck constant is bigger?

Schrödinger’s cat, the thought experiment, makes it seem like as if measurement can cause a system to stop being in a superposition of states and become either one of the states (collapsed). So does ...
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1k views

Uncertainty relation and Energy-Position interference

How would you prove that the simultaneous measurements of position and energy are not subject to interference? I was thinking in calculate the commutation relation between $x$ and $H$ (Because $\Delta ...
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1answer
470 views

Band Structure and Carrier Recombination/Generation

So i've been a bit confused, looking at PN junction, semiconductors and the like (trying to nail down how exactly semiconductors work, transistors and such). I've read the wiki on band structure ...
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4answers
929 views

Do multiple electrons exist during superposition?

Wikipedia says: Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular, theoretically ...
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1answer
710 views

Wave functions for three identical fermions

I would like to express the wave functions for three identical particles, each with orbital angular momentum $L=1$ and spin angular momentum $S=1/2$, in terms of single-particle wave functions. In ...
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3answers
415 views

Is this interpretation of $\psi=\frac{1}{\sqrt{\pi a^{3}}}e^{-r/a}$ correct?

Apologies if this is stating the obvious, but I'm a non-physicist trying to understand Griffiths' discussion of the hydrogen atom in chapter 4 of Introduction to Quantum Mechanics. The wave equation ...
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3answers
3k views

What does the quantum state of a system tell us about itself?

In quantum mechanics, quantum state refers to the state of a quantum system. A quantum state is given as a vector in a vector space, called the state vector. The state vector theoretically ...
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Scattering in quantum wires

I'm working on a project involving scattering of particles in networks of quantum wires off of point scatterers. The problem that I am having is that even in fairly simple configurations of quantum ...
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82 views

Topological Solitons and the Higgs Condensate entanglement

While focusing on resolutions to the Firewall controversy, and the possible implications of the Higgs field as it relates to the issue, the possibility of using EPR correlations in the Higgs ...
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231 views

Non-destructive measurement of qbits

Yale news "New qubit control bodes well for future of quantum computing" (Original paper) says: "The Yale physicists successfully devised a new, non-destructive measurement system for observing, ...
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756 views

Why shouldn't the uncertainty principle be interpreted as an observer effect?

The Heisenberg Uncertainty Principle suggests that the more precisely the position of a particle is measured, the less precisely its momentum can be known, and vice versa. $$\sigma_x \sigma_p \geq ...
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672 views

Vector Potential and Gauge Invariance in Quantum Mechanics

In classical electromagnetism, we are allowed to use gauge invariance through the argument that the only physical observable fields are the $E$-field and the $B$-field. So in that sense the scalar ...