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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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
19 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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votes
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
votes
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
78 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. ...
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1answer
36 views

Quantum information [closed]

What are the basic laws and formulas that founded the sub field of Quantum Information? What's the best reference available (masters level)?
3
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0answers
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
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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
28 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}= ...
7
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
57 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
99 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.
0
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0answers
33 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 ...
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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
65 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
votes
2answers
198 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 ...
0
votes
1answer
18 views

Why characteristics graph of Geiger Muller Counter always goes up?

The characteristics graph of Geiger Muller Counter always keeps going up and does not drop down . It may remain constant over an interval but does not drop down on the graph scale. Why it does not ...
10
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1answer
149 views

What is known about the hydrogen atom in $d$ spatial dimensions?

In a first (or second) course on quantum mechanics, everyone learns how to solve the time-independent Schrödinger equation for the energy eigenstates of the hydrogen atom: $$ ...
0
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0answers
29 views

Fermi's golden rule and the DoS of scattering states

Can the Fermi's golden rule $$\Gamma_{fi} ~=~ \rho(E_f) \frac{2\pi}{\hbar} |M_{fi}|^2$$ be applied for transitions of discrete states to scattering states? If yes, then what should the density of ...
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votes
1answer
100 views

Ground state energy of spin 1 particle

So I have this Hamiltonian for a particle with spin 1: $$ H=aS_{z}^2+\frac{\hbar\omega}{\sqrt2}S_{x}$$ where ($a$ and $\omega$ both real constants): $$ S_{z}=\hbar\begin{pmatrix} 1 & 0 & 0 ...
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1answer
37 views

Why the constancy of an observable w.r.t time depends on whether it commutes with $H$ or not?

I have been reading Modern Quantum Mechanics by J.J.Sakurai. Under the chapter Quantum Dynamics, the author says if an observable $A$ initially commutes with the Hamiltonian operator $H$, then it ...
0
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1answer
21 views

CNOT gate with trapped ions

I'm interested in knowing the structure of a CNOT gate, in quantum computing. THe problem with that is, that I've read how the structure of a nuclear quantum computer works, but I still don't ...
0
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0answers
43 views

Why is the Hermitian conjugate of the Fourier transform of an operator not the transform of the Hermitian conjugate? [migrated]

It is defined that: \begin{align} O(\omega)&=\frac{1}{\sqrt{2\pi}}\int O(t)e^{-i\omega t} \mathrm{d}t \tag{1} \\ O^{\dagger}(\omega)&=\frac{1}{\sqrt{2\pi}}\int O^{\dagger}(t)e^{-i\omega t} ...
3
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1answer
42 views

Behavior of atom's wave packets in a gas

It is my understanding that the wave packet of a free localized particle spreads with time. My question is what is the best description of the particles in a gas inside a closed container: Do they ...
0
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1answer
53 views

Magnetic field induce photons?

So silly question, can a oscillating magnetic field excite electrons around atoms such that they produce photons (In other words can an applied magnetic field increase the energy level of electrons ...
0
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0answers
49 views

What knowledge do I need to learn Quantum Physics? [duplicate]

I have a quick question. What prior knowledge do I need to learn and understand quantum physics. For example, what type of math do I need to know, what level of physics, etc.
0
votes
1answer
33 views

How to check if a Hamiltonian is PT symmetric or not?

Consider the Hamiltonian $$H=p^2+ix^3+ix.$$ This paper by Carl M bender claims this is a $PT$ symmetric Hamiltonian. In this he describes $PT$ symmetry as parity $P$, whose effect is to make ...
10
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1answer
984 views

Can't quantum teleportation be superluminal some percentage of times?

I apologize if this is a really silly question. In the (textbook) quantum teleportation algorithm, in the step right after Alice has measured her system but before she has sent her classical ...
0
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0answers
20 views

Overtone Transition Probability

For an anharmonic potential, like the morse potential, higher order transitions (overtone) with $\Delta n=\pm2,\pm3,..$ are allowed. How do I calculate the probability $P$ for such transitions? My ...
0
votes
1answer
72 views

Propagating a Gaussian wavepacket backwards in time

So, I'm following the MIT OCW lectures on 8.04 quantum mechanics by Prof. Allan Adams. I have the expression for the probability distribution of a gaussian wavepacket for a free particle situation. No ...
0
votes
1answer
36 views

Rate of the increase of width of a Gaussian wavepacket

So, I'm following the MIT OCW lectures on 8.04 quantum mechanics by Prof. Allan Adams. I have the expression for the probability distribution of a gaussian wavepacket for a free particle situation. No ...
3
votes
2answers
116 views

Where are the photons coming from?

Particles and Antiparticles can annihilate, and they are completely destroyed in the process, which creates photons. From wikipedia: ...
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2answers
49 views

What makes the probability distribution of a wavefunction in QM intrinsic? [closed]

I know that the usual interpretation of the wavefunction in QM is that it´s associated with a probability distribution of measurable quantities. Not a deterministic probability (like the probabilities ...
12
votes
3answers
2k views

How come light waves don't get caught and absorbed by the electrons of oxygen atoms in the in air?

Shouldn't air be opaque since instead of coming into our eye, the lightwaves get caught in the electrons? If oxygen does absorb light waves, how come air is not hot and you can see through it? The way ...
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votes
1answer
51 views

Does quantum uncertainty effect strings? [closed]

If the bases of string theory is that specific vibrations in strings create specific dimensions, how can these vibrations exist within the parameters of quantum uncertainty? Wouldn't the uncertainty ...
1
vote
1answer
79 views

How is no-conspiracy theory compatible with determinism? [closed]

Bell's theorem states that any physical theory that incorporates local realism and the no-conspiracy assumption cannot reproduce all the predictions of quantum mechanical theory. Hence, we cannot ...
2
votes
1answer
56 views

Expressing eigenstates of $\mathbf{L}^2$ and $L_z$ in terms of the Cartesian eigenstates $|n_x\, n_y\, n_z\rangle$

I want to express the degenerate eigenstates of the three-dimensional isotropic harmonic oscillator written as eigenstates of $\mathbf{L}^2$ and $L_z$, in terms of the Cartesian eigenstates $|n_x\, ...
2
votes
1answer
33 views

Obtaining wave function from field equation

The Dirac field $\Psi(x)$ satisfies the Dirac equation $$(i\gamma^\mu\partial_\mu-m)\Psi(x)=0$$ When we quantize, each of the four components of the Dirac field becomes an operator that creates or ...
0
votes
0answers
35 views

Rotations acting on quantum states

Suppose I have a free relativistic massive particle described by a state $|p,\sigma\rangle,$, with $p^\mu=(p^0,0,0,p^3)$, so that $P^3|p\rangle=p^3 |p,\sigma\rangle$ and ...
0
votes
2answers
51 views

Can conducting electrons in a metal be modeled at all as classical particles?

I have seen computational models that treat the highest energy electrons in a conducting metal as classical particles in a plasma, the ions being held in place with some sort of heuristic ...
0
votes
0answers
62 views

What does it mean to take a derivative with respect to $\hbar$?

Problem 6.32 of Griffiths Introduction to Quantum Mechanics, 2ed is In part (b), we take a derivative with respect to $\hbar$. Since $\hbar$ is a constant, what does it mean to take a derivative ...
3
votes
2answers
46 views

Introducing a phase, what changes?

This question is related to: Mach-Zehnder interferometer and the Fresnel-Arago laws Let us say we have unpolarised wave taking the form: $$\psi=\psi_0 e^{i(kx-\omega t)+i\phi(t)}$$ Where $\phi$ ...
3
votes
1answer
37 views

Spread of the energy levels and sharp energy eigenvalues of the Schrodinger equation of the H-atom

Solving the Schroedinger equation for the H-atom (or any other system, say a particle in a box, or harmonic oscillator or anything), we obtain the energy eigenvalues are sharp with no spread. However, ...
5
votes
5answers
133 views

What is the explanation for the interference patterns in MWI?

In Young's double-slit experiment, MWI states that in some "worlds" the particle goes through one slit, and in others it goes through the other. If this is so, why do we get an interference pattern? ...
2
votes
0answers
35 views

Is electron phonon interaction important away from fermi surface?

In weak coupling superconductor, the effective electron phonon interaction can be written as $$ H_{eff}=\frac{1}{2}\sum_{q,k_1,k_2,\sigma_1,\sigma_2} V_{k_1,q}C^{\dagger}_{k_1+q,\sigma_1} ...
0
votes
1answer
30 views

Why is the interaction energy of the electrons in an atom positive?

Consider a simple Hamiltonian for the Helium atom (where $e'^2 = e^2/4\pi \epsilon_0)$: ...