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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What is the name of basis states of bulk k.p Hamiltonian?

A k.p Hamiltonian for a bulk material can be represented by 8x8 matrix in basis of $|S\uparrow\rangle$, $|S\downarrow\rangle$, $|X\uparrow\rangle$, $|Y\uparrow\rangle$, $|Z\uparrow\rangle$, ...
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2answers
124 views

About de Broglie relations, what exactly is $E$? Its energy of what?

Well, you may know de Broglie relations, here they are: $$ E = h\nu, \quad\quad p = \frac{h}{\lambda} $$ My question is simple: What exactly is $E$? Is it the total energy? Maybe only kinetic energy? ...
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1answer
40 views

Global and relative phases of kets in QM

In one of the questions I'm trying to solve it is asked to, first, compute probabilities for the respective results of the Stern-Gerlach measurements performed on each state $\lvert\psi_1\rangle$, ...
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32 views

Probability of measuring a pure qubit state after some unitary rotation [closed]

Suppose I have the prepared state $$|+\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}$$ and the unitary $Z_{\pi/2}$ which rotates a state in the Bloch sphere by $+\pi/2$ about the $z$-axis. As I ...
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1answer
37 views

Drive term for a Jaynes-Cummings like hamiltonian

When reading articles on CQED or atomic physics, I often encounter the Jaynes-Cummings Hamiltonian, which in the simplistic form I will write down as: $$H = \hbar \omega_c a^\dagger a + \hbar ...
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1answer
84 views

Dirac Equation in RQM (as opposed to QFT) is written in which representation?

In introductory Quantum Mechanics treatments it is common to see the Schrödinger's equation being written, simply as: ...
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1answer
49 views

Why do some stars become end up as black holes? [closed]

The answer involves the gravity and the internal pressure within the star. These two things oppose each other -- the gravitational force of the star acting on a chunk of matter at the star's surface ...
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1answer
32 views

What are “interferences of higher order” in the context of Born rule and triple-slit diffraction?

This question relates to the paper commented in this 2010 article. The paper itself is Ruling Out Multi-Order Interference in Quantum Mechanics; it is the discussion of a triple-slit interference ...
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2answers
106 views

Do conservation laws contradict quantum mechanics? [closed]

Take for example the double-slit experiment interpreted in the Copenhagen sense. The particle leaves as an object with mass, yet passes through the slits as a massless wave, only to collapse again as ...
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2answers
58 views

Why does electron respond almost instantaneously on nucleus' displacement due to the difference in mass of it and the nucleus?

In Born Oppenheimer Approximation, we take note of the great difference between the mass of the electrons and nuclei. But, I have not been able to understand this statement quoted from Molecular ...
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40 views

What are Black holes exactly? [closed]

A Black Hole is a very large rip in the atmosphere that opens after to many shuttles have traveled into space. It happens after about 5 million years of shuttles traveling in and out of spaces ...
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2answers
134 views

Rigorous definition of density of states for continuous spectrum

For operators with pure point spectra it is clear how to count number of states corresponding to a given eigenvalue - one can just calculate the dimension of eigenspaces. I am wondering how to do it ...
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41 views

Quantum tunneling and the Gamow Factor

I've seen the equation for the probability of particles overcoming the Coulomb Barrier in the following form: $$P(E_G)=\exp\left[-\sqrt{E_G/E}\right]$$ Where I'm using the numerator $E_G$ as the ...
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1answer
78 views

Eigenstates of position and momentum operators in QM

In Griffiths pages 103-105 "Introduction to Quantum Mechanics" 2nd editiion he states that the eigenfunctions of the position and momentum operators are $$g_y(x) = \delta(x-y)$$ where the eigenvalue ...
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5answers
186 views

Where does $\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$ come from?

It's a very basic question, where does the relation $$\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$$ for any square integrable $\psi(x)$ come into existence? Some texts I found states that the above ...
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0answers
84 views

“Wonderful weirdness” - I want to know whether I am a human being or something else [closed]

EDIT: after moderators' comment below, I am adding this paragraph: This post is a partial satire. My question was how is this possible that, an object as big as ~50 micron is vibrating and not ...
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1answer
32 views

understanding thermal radiation in a conductor, gas and insulator

Context: I was in my bliss of ignorance and happiness when I was taught that quantum mechanics was about nice discrete values of energies. Now I am introduced the idea of Fermi Energy in a block of ...
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1answer
44 views

Gaining some intuition: Photon bunching

This is a very easy question: I'm in need of some intuition on the fact that, e.g. thermal sources, produce bunched photons. It is very easy to "undertand", without any quantum mechanics, why single ...
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1answer
93 views

Von Neumann entropy of mixtures of coherent states

I'm trying to calculate the Von Neumann entropy of statistical mixtures of coherent states. The problem is that such states are in general non-Gaussian, so one cannot follow the formalism developed ...
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1answer
61 views

Is superposition state of SHO ever observed? [on hold]

Feynman says, "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." So, is superposition state of Simple ...
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1answer
111 views

After proving that the photon remains stationary in the fourth dimension, must we conclude that the fourth dimension is moving at c? [closed]

Firstoff, in his general relativity Einstein showed that dimensions could bend, curve, and move. This is an experimentally proven fact. Dimensions can, and do, move. In an earlier post we ...
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4answers
161 views

Is time an observable in Relativistic Quantum Mechanics?

Relativistic Quantum Mechanic is based, as far as I know, in the Dirac Equation. Now, the Schrödinger equation, in the abstract state space takes the form: $$i\hbar ...
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1answer
7k views

If we had a “perfectly efficient” computer and all the energy in the Milky-way available, what number could it count to?

The idea for this question comes from an example in cryptography, where supposedly 256-bit symmetric keys will be enough for all time to come (brute-forcing a 256-bit key is sort-of equivalent to ...
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0answers
42 views

Does anyone know how/where I could view the Double slit experiment in person? [closed]

I want to see the double slit experiment in person! The one where the observer effects the wave/particle state of an electron. Where would I be able to view this experiment? Is it on display in any ...
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2answers
69 views

Is there any atom which is dia-electric?

Take an atom. Suppose we impose some magnetic field on it. For some atoms, the energy increases---this is a phenomenon of diamagnetism. The question is, how about an electric field? Can the energy ...
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2answers
105 views

Are electron densities and electrostatic forces possibly responsible for gravity? [closed]

The idea I had was that whilst electrons usually orbit within the Bohr radius of atoms there is a chance of them appearing significantly further away than that, meaning that if all the electrons in ...
6
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1answer
143 views

Question on doing the integral for Fermi golden rule

Today in the lecture, my professor did something which confused me As an example, we consider the photoelectric effect, in which an electron bound in a Coulomb potential is ionized after ...
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0answers
72 views

Parity operators and spin

Consider the following excerpt from Weinberg's Lectures on Quantum Mechanics: I follow everything up until the last statement in the excerpt. In fact, from other things I've read, it seems that one ...
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2answers
54 views

Atom Particles Relationships

I am an agriculture student, and we study tons of chemistry, and despite I took the exams I still have a good doubt on atoms. Through my studies I would say electrons are very tiny containers of ...
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1answer
37 views

Why can one suppose $\alpha^i$ and $\beta$ matrices in the derivation of the Dirac Equation?

On the derivation of the Dirac Equation one usually supposes that it is possible to write $$E = \mathbf{\alpha}\cdot \mathbf{p} + \beta m.$$ One then deduces that in order to have $E^2 = p^2+m^2$ it ...
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44 views

Local Phase Transformation of the Dirac equation

The Dirac Equation ("free Dirac") is a relativistic Equation of Motion (EoM) for a free ($V=0$) Spin $1/2$ particle (like an electron). The free Dirac equation is invariant under global phase ...
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1answer
46 views

Fermi energy of electron gas with electrostatic interaction

I have been given the following exam question and am unsure how I would go about solving it: Consider the case of a one-dimensional metal, consisting of a chain of $N$ positive charges $+q$ ...
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30 views

On LOCC operations

I am trying to learn quantum information theory. Suppose we have a bipartite (as well as multi-partite) quantum system $H_A \otimes H_B$. What is a LOCC map $\phi: \mathcal{B}(H_A \otimes H_B) ...
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36 views

How to generalize the Bohr-Sommerfeld quantization condition to more dimensions?

As in the title-how to consider this condition on e.g. a polar or spherical coordinate system, with two or three dimensions? Which different methods I can use? EDIT: the coordinate system doesn't ...
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2answers
171 views

How do we explain the existence of liquids, from a mathematical or computational perspective? [closed]

This post asks why matter exists in three phases. Most of its answers explain the existence of liquids with some variant of the following: liquids happen when thermodynamic conditions, temperature ...
2
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0answers
70 views

Analyzing the free-particle kernel [closed]

I recently began studying the theory of path integrals from the book by Feynman and Hibbs. The Problem $3.6$ asks to give an argument to show that $F(t_b,t_a)$ depends only on $t_b-t_a$. ...
2
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3answers
109 views

Would a particle the size of a neutron, if it had enough mass, collapse into a blackhole?

For example, a neutron is a particle that occupies a certain volume. If you pack enough mass into that volume, it would collapse into a black hole (I assume there is not enough mass now). At least if ...
3
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2answers
101 views

What happens when two wavefunctions meet?

Apologies for the over-broad question(s), but I'm having a hard time finding out where to look to answer these myself: If a particle is a wavefunction describing a probability amplitude distributed ...
3
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0answers
48 views

Why is diproton unstable? [duplicate]

Diproton is an isotope of helium without any neutrons. It commonly forms in the Sun, where protons are fused constantly. However, it is extremely unstable, and will revert back to two protons almost ...
2
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0answers
99 views

Modern interpretation of wave-particle duality

As far as I understand, in the early days of quantum theory there was quite a lot of debate over how to interpret what it meant for a quantum mechanical object to exhibit both wave-like and ...
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2answers
71 views

Variation of schrodinger cat replaced by quantum computer

In the "classical" imaginary Schrodinger's cat experiment, which seems to be no longer serious, or at least irrelevant, by many (some?) people, everything is explained away by decoherence. Now, let ...
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0answers
48 views

Manipulating tensors in relativistic quantum mechanics

I was doing a problem that involved showing a Heisenberg equation of motion was consistent with the Dirac equation. The question involved a lot of algebra which was generally fine but something done ...
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0answers
28 views

What will be the wavefunction for two 'semidistinguishable" atoms?

So say I have 2 hydrogen atoms in a box, and it is assumed there is no interaction Hamiltonian. One has it's electron in energy eigenstate n=0 in the hydrogen atom, the other is in a superposition of ...
1
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1answer
29 views

Quantum Mechanics State Proportional to x

I have a particle in a 1D infinite potential well. i.e $$V(x)=\left\{ \begin{array}{c} V(x)=0 \text{ for } |x|<a \\ V(x)=\infty \text{ for } |x| \geq a \\ \end{array}\right. $$ I ...
0
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1answer
41 views

Infinite depth potential well (energy probability) [closed]

Consider a particle in an infinite depth potential well of length 2a. The particle is in a state in which it is described by the wavefunction $\psi (x)=A(a^2-x^2)$ for $-a\leq x \leq a$ with a ...
3
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2answers
69 views

Simple question about decoherence

In simple terms, decoherence is the mechanism through which a quantum system in superposition that interacts with the environment undergoes a quick "apparent collapse" and is no longer found in ...
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2answers
164 views

Is the $i$ in QM a time component in disguise?

In SR, it is possible to replace the Minkowski metric $\eta_{\mu\nu}$ with a (pseudo) euclidean metric $\delta_{\mu\nu}$ provided that time is measured in imaginary units. I was wondering if the same ...
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20 views

Is there a framework in which observables are blades in a Clifford algebra?

Just wondered whether the noncommutativity of observables could be linked to the manifestation of an higher dimensionality (as the geometric interpretation of the Grassman outer product, which is ...
2
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0answers
59 views

Measurement of $L_z$ in a state which includes spin

I'm working through a problem on finding probabilities for measurements performed for quantities associated with one electron in three dimensions with spin. In that case we know that the state space ...
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1answer
66 views

Under what condition is angular momentum conserved in both classical and quantum physics?

Classically, angular momentum is only conserved in a central potential by considering the torque (correct me if I am wrong). In quantum mechanics, it is also true, isn't it? If this is the case, ...