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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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
41 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 $+q$ ...
3
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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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35 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 ...
6
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2answers
166 views

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

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
69 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
105 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
91 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
95 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
69 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
32 views

Magnetism shown by the electron [closed]

In a hydrogen atom, can you derive the expression for the magnetic field at the centre of the atom produced by an electron in the nth orbit.?
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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
28 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
67 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 ...
1
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2answers
125 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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0answers
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 ...
1
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1answer
65 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, ...
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0answers
113 views

What was Dirac's clear intuitive understanding of the electron? [closed]

There have been some recent questions concerning de-Broglie Bohm theory, such as this and this. The latter asked if Dirac's argument against classical mechanics stands in contradiction to Bohm's ...
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2answers
98 views

Does $[A^2,B]=0$ imply $[A,B]$=0? [closed]

The commutator $[A^2,B]$ can be written as $A[A,B]+[A,B]A$. So if $[A,B]=0$, $[A^2,B]$ is also zero. But is the converse also true? If $[A^2,B]$ is given to be zero, then is [A,B]=0? Let $C=[A,B]$. ...
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0answers
66 views

Quantum mechanics and probability quick question [closed]

After reading some articles about quantum mechanics and probability I came up with a conclusion - there is a nonzero probability of existence for every world which is deemed as a fantasy world, with ...
3
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1answer
41 views

Hydrogen Ground State Energy

Using the non-relativistic Schrodinger equation, the energy levels for hydrogen are found to be $E_{n} = -\frac{1}{2n^2}mc^2\alpha^2$. Using the relativistic Dirac equation, the energy levels for ...
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3answers
80 views

Why identical particle states are multiplied?

In case of identical particles we multiply the individual wave functions of the particles to get the system wave funtion. But why are we not adding? Or performing any other operation to get the system ...
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0answers
26 views

Can linear combinations of expectation values be considered a valid expectation value?

I ask this question with Bell's paper in mind. I certainly don't hope that is actually necessary for anyone to look at but here is the link anyway: ...
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2answers
93 views

What is the physical states in Heisenberg picture?

The physics states in Quantum mechanics is represented by vectors in Hilbert space, however in Heisenberg's picture, the equation of motion $$ \frac{d}{dt}A_H(t) = ...
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1answer
88 views
+50

In semiconductor devices, why is quantum tunneling “fast”?

I'm reading up on semiconductor devices that rely on quantum tunneling, such as the tunnel diode and the TFET. The big advantage of these devices is apparently that "quantum tunneling is extremely ...
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2answers
73 views

Does uncertainty exist without consciousness? [closed]

How can uncertainty exist without conscious beings calling something uncertain? When you look at the uncertainty principle, it only makes sense if consciousness collapses, disturbs, interfere's with ...
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0answers
48 views

Differentiation, Dirac operator, Hermitian [duplicate]

I am trying to prove the hermitan property of Dirac operator $$\gamma^{\mu}D_{\mu}=\gamma^{\mu}(\partial_{\mu}+iA_{\mu}).$$ The underlying space time i assumed is euclidean ...
0
votes
1answer
22 views

Rotating wave approximation for two coupled resonators and a drive

I'm having some trouble with what I think should be an easy calculation. On qutip.org/docs/2.2.0/examples/me/ex-25.html they calculate the steady state for a master equation, more specifically they ...
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1answer
57 views

Eigenvalues and states of hamiltonian [closed]

A quantum mechanical system is described by a two dimensional Hilbert space of states, spanned by an orthonormal basis {|1>, | − 1>}, with the following Hamiltonian: $ H | 1> = | ...
2
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2answers
163 views

What's wrong with this Hamiltonian matrix?

Suppose we have a Hamiltonian matrix: $$H= \begin{pmatrix} 0&\tanh x-\partial_x\\ \tanh x+\partial_x&0\\ \end{pmatrix} $$ Obviously, $H^\dagger_{ij}=H_{ji}$. Two of the eigen-states of this ...
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0answers
13 views

mean energy as a function of nuclear charge Z

I'm stuck on finding the E(Z) part, what I have is $\ \langle E \rangle = E(Z) = \langle p_1^2 + p_2^2 \rangle/2m_e - \langle 1/r_1 + 1/r_2 \rangle Ze^2/4\pi\epsilon_o + \langle 1/r_{12} ...
6
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2answers
80 views

Understanding Gibbs $H$-theorem: where does Jaynes' “blurring” argument come from?

According to this Wikipedia article, the $H$-theorem was Boltzmann's attempt to demonstrate the irreversible increase in entropy in a closed system starting from reversible microscopic mechanics. ...
3
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31 views

Microscopic interpretation of magnetization in a 2D electron gas

I'm studying the de Haas-Van Alphen (dHvA) effect in a 2D free electron gas, and I have a problem to interpret the microscopical meaning of the flip of magnetization during the dHvA oscillation. My ...
3
votes
1answer
73 views

Peculiarity about a system of three electrons

Consider three (or any number bigger than 2) electrons without spatial degrees of freedom, thus the only degree of freedom is the spins. The Hilbert space is then formed by the tensor product of the ...
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0answers
30 views

Solving Schrodinger equation in magnetic field with mixed gauge condition [closed]

Consider electrons in magnetic field at low temperature, solve the Schrodinger equation to find out Landau level for the vector potential chosen as follows $$ \vec{A}= ...
8
votes
4answers
1k views

Why does an electron shell further away from nucleus has higher energy level?

Using electrical potential energy $V=\frac{1}{4\pi \varepsilon_0} \frac{Q_1 Q_2}{r}$ , a particle further away from nucleus has lower magnitude of energy. Using Coulomb's law, a particle further away ...
3
votes
1answer
61 views

Squeeze operator

If $\phi(x)$ is an arbitrary normalized function, and $S$ the squeeze operator, $$ S=e^{\frac{\mu\cdot h}{2\pi}(a^{\dagger2}-a^{2})} $$ with $\mu \in \mathbb R$. How can I find the value and the ...
0
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0answers
30 views

Application of the concept of hidden variables in Bell's article

This question is with regards to Bell's article, "On the problem of hidden variables in quantum mechanics." I am confused about how hidden variables (I concept I understand vaguely but fail to see ...
1
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2answers
100 views

Is Everything Vibrating?

It is often said that "everything is in a state of constant vibration". What led to this statement? And can I get any source of this statement that I can cite? Thank you.
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0answers
34 views

Commutation relation for Weinberg's rigid rotator

In Weinberg's discussion of the rigid rotator, (section 4.9 of Lectures on Quantum Mechanics), he defines a rotation operator in terms of the position operator in the laboratory frame and the (assumed ...
0
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0answers
46 views

Feynman's Path Integral Approach: The Complex Exponentiated Action [duplicate]

I'm working on a project covering Feynman's Path Integral Approach. I'm having trouble intuitively grasping what motivates the introduction of the expression $e^\frac{iS}{\hbar}$, where S is the ...
0
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0answers
36 views

Help needed for Simple derivation for duality of matter

A teacher told showed me a way to derive an equation which shows the duality of matter. We know, $E=hc/\lambda$. and $E=mc^2$ So, $hc/\lambda=mc^2$ We get, $p$ ( momentum ) = $h/\lambda$. How ...
1
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0answers
46 views

What is the cause of discrete or quantized energy levels in an atom? [duplicate]

I understand how it is that electrons move from one energy state to another, however I've not been able to find anywhere that describes why an atom has any particular states. Why should an atom of ...
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1answer
66 views

Can a strange property of entangled particles be expressed as a physical analogy in our everyday world or is this argument suspect?

If it is possible for one to find a physical analogy in our everyday world to one of the strange properties of entangled particles does this mean that a similar concept should be considered at the ...
3
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2answers
199 views

Why do the ladder operators in harmonic oscillators work?

The Hamiltonian can be diagonalized by transforming $x$ and $p$ to $a$ and $a^\dagger$. I understand how one proceeds from there to find the spectrum of $a^\dagger a$, the ground state $|0\rangle$ and ...