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 quantum-field-...

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3
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1answer
225 views

$N$ coupled quantum harmonic oscillators

I want to find the wave functions of $N$ coupled quantum harmonic oscillators having the following hamiltonian: \begin{eqnarray} H &=& \sum_{i=1}^N \left(\frac{p^2_i}{2m_i} + \frac{1}{2}m_i\...
0
votes
0answers
49 views

Radiation by accelerating charge in quantum physics

We know that in classical physics if a point charge accelerates in an inertial frame$^\dagger$, then it will radiates. I wonder how radiation by accelerating charge is described in quantum physics. I ...
1
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2answers
132 views

Mathematical confusion in quantum mechanics

During a class about Ehrenfest theorem, my teacher use an equation to proceed its derivation (to prove $\frac{d<r>}{dt}=\frac{<p>}{m}$ ) and that is: $$\int{x\psi\nabla^2\psi^*}d\tau=\int{\...
4
votes
2answers
367 views

Off-diagonal elements of Hamiltonian matrix $H_{12}$ & $H_{21}$: energy of transition from $|1\rangle$ to $|2\rangle$ or amplitude of transition?

$$ \newcommand{\k}[1]{\left| #1 \right\rangle} \newcommand{\dd}[1]{\frac{d #1}{dt}} $$ In a Hamiltonian Matrix like this: $$H = \begin{pmatrix} E_{11} & E_{12} \\ E_{21} & E_{22} \end{...
0
votes
1answer
39 views

Trying to visualize virtual particle behavior near “real” particles

I hope this isn't too clumsy a question, but I'm trying to figure out if my way of thinking about virtual particles is reasonably OK or completely wrong. This question got me thinking about it ...
1
vote
2answers
116 views

Commutator of position and momentum

I'm reading Sakurai's Quantum Mechanics. One of the problem in the book asks to use the relation $$ \langle{x}|p\rangle=\frac{1}{\sqrt{2\pi\hbar}}e^{\frac{ipx}{\hbar}} $$ to evaluate $\langle{x}|[X,P]|...
0
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1answer
36 views

Are there any other tests demonstrating wave properties besides interference and diffraction?

Are there any other tests demonstrating wave properties besides interference and diffraction? How about refraction? Does it show wave properties also?
0
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1answer
61 views

Hermitian Conjugate in Spherical Coordinate System [duplicate]

Help me find $\hat{B^\dagger}$, when we know that $$\hat{B}=i\frac{d}{dr}$$ with the condition that $\hat{B}$ is defined in spherical coordinates. My approach: $$ \langle\psi|\hat{B}\psi\rangle=\int_{...
1
vote
0answers
78 views

Connection between Lindhard susceptibility and Free energy

I've encoutered a few times, but I never got an explanation for it... How is the spin-dependent Lindhard function for the dynamical susceptibility of an electron gas $$ \chi_{\sigma,\sigma'} (q, \...
2
votes
1answer
202 views

Superposition of two wave functions of different Hilbert spaces

I am trying to think of this problem for quite some time. Let's say, we have two sets of wave functions $\lbrace|\psi\rangle\rbrace$ and $\lbrace|\phi \rangle\rbrace$ and they belong to two different ...
0
votes
2answers
342 views

Hermitian conjugate of differential operator

Help me find $\hat{B^\dagger}$, when we know that $$\hat{B}=i\frac{d}{dr}$$ with the condition that $\hat{B}$ is defined in spherical coordinates. My approach: $$ \langle\psi|\hat{B}\psi\rangle=\int_{...
0
votes
1answer
36 views

The elementary particles uniformity and its limits in the context of matter [closed]

We know that matter particles are uniform, i.e. they are absolutely identical (1, 2, 3). Particles of various properties are uniform. But if we look at bigger matter elements, when and how does the ...
0
votes
2answers
152 views

Could I turn into a nuclear bomb?

Just out of curiousity, could the nuclei of our atoms split via quantum tunnelling, thereby leading to nuclear reactions and ultimately turning us into atomic bombs? I know that this is near-...
0
votes
0answers
86 views

Gromov: 2+2=4 and Quantum Mechanics

I was watching a talk by the mathematician Gromov, and was perplexed by some things he said: 1) that 2+2=4 is related to Archimedes cylinder-sphere theorem, and 2) that this is related to the ...
0
votes
0answers
44 views

How does the collapse of one wavefunction affect another wavefunction?

Suppose we have an experiment with half silvered mirrors in a laboratory. We are shooting photons at these mirrors and measuring where the photons end up. The dynamic system have associated with it a ...
0
votes
0answers
51 views

Numerical approach to Mean Field Hubbard Model

I am trying to produce the phase diagram of a 2D Hubbard model on a Lattice for spineless bosons. The hamiltonian of the problem is: $$ H = -t\sum_{<i,j>}(b_i^+b_j + c.c.) +U\sum_i \frac{n_i(n_i-...
1
vote
1answer
176 views

How/Why did Feynman relate the element of Hamiltonian matrix $H_{12}$ to the amplitude to go from $|1\rangle$ to $| 2\rangle$?

$$ \newcommand{\bk}[2]{\left\langle #1 | #2 \right\rangle} \newcommand{\ket}[1]{\left| #1 \right\rangle} \newcommand{\bra}[1]{\left\langle #1 \right|} \newcommand{\biik}[3]{\left\langle #1 | #2| #3\...
4
votes
0answers
132 views

What is the rigorous description of scattering in relativistic QFT?

The first conundrum is what picture of QM to choose, in order to describe such a scattering. Unlike in non-relativistic QM, in RQFT the three all-known pictures are not at all equivalent. The ...
4
votes
1answer
152 views

What is the description of measurement in the Heisenberg picture?

In all the books I've read this picture is presented only briefly, by essentially saying that in the HP the whole time dependence is assigned to the operators (representing observables), whereas the ...
1
vote
2answers
122 views

Derivation of $E=h\nu$?

I found this question here and the answers got me thinking. Take a case where $\Psi(x,t)$ is the linear combination of two eigenvectors of a charged particle: $\Psi(x,t)=c_1\psi_1e^{-iE_1t/\hbar}+...
2
votes
2answers
176 views

Existence of bound states in 3D Yukawa potential

For a 3D Yukawa potential $$ V(r) = - \lambda { e^{-Mr} \over r}. $$ Bargmann's upper bound can be read as necessary condition for the existence of at least one bound state; we want $N_l>1$ and ...
1
vote
1answer
40 views

Particle-antiparticle behaviour

I am trying to understand several particle-antiparticle concepts and there are questions that are not answered in any literature: Hawking's radiation: what happens if classic particle of particle-...
2
votes
1answer
689 views

Why can't electrons be found inside the nucleus if there are infinite number of orbitals?

If there are an infinite number of orbitals, we can assume, that they can be present in any point in space. If that is correct, why do we not find electrons in the nucleus? I study in high school. ...
1
vote
1answer
71 views

Hubbard model in the t>>U limit

I know one can obtain the t-J model from the Hubbard one by taking the limit $t\ll U$ in the following Hamiltonian: $H= -t\sum_{i\neq j}a_{i\sigma}^\dagger a_{j\sigma}+U\sum_i n_{i\uparrow}n_{i\...
1
vote
0answers
79 views

The second order scalar quartic field theory Feynman diagrams

I'm trying to find the second order Feynman diagrams for the scattering of a scalar phion, described by the Lagrangian $$ L = L_0 + L_I \\ L_0 = \frac{1}{2}[\partial_{\mu} \phi(x)]^2 - \frac{1}{2}m^2 ...
0
votes
2answers
82 views

Uncertainity principle and double slit experiment?

My Understanding of uncertainty principle goes that if some particles are in same state, then their measurement of certain property (say $x$ and $p$) will be different for different particles. ...
-2
votes
1answer
88 views

Does the uncertainity principle actually attack determinism? [closed]

It's not really clear to me how does QM attacks determinism. It sure attacks computability, which is a component of newtonian, naive determinism, but it's often claimed to destroy determinism itself (...
0
votes
1answer
104 views

Normalizing a wave function [closed]

A particle with mass $m$ is moving in one dimension. The wave function of the particle is $$\Psi(x,t)=Axe^{-(\sqrt{km}/2\hbar)x^2}e^{-i\sqrt{k/m}(3/2)t}$$ for $-\infty<x<\infty$, where ...
3
votes
1answer
73 views

How can quantum confinement be obtained?

I have been reading about quantum confined systems. That is, systems of one or two particles or atoms inside a region of space of radius R where potential energy is, say V(r), for r < R and ...
7
votes
2answers
213 views

The role of anharmonic oscillator(s) in Heisenberg's 1925 paper

I am talking about the most famous paper of Heisenberg, which I know from the translation of van der Waerden (Sources in Quantum mechanics, North Holland, 1967). After introducing matrix mechanics ...
0
votes
3answers
205 views

What is the prerequisite for learning quantum mechanics

I want to learn quantum mechanics myself and when I open books about them I see weird symbols and different types of mathematical formulas and physics concepts. So what should I first study in ...
0
votes
1answer
70 views

Why does current vary continuously with potential in the photoelectric effect?

In the photoelectric effect, for a given intensity and frequency of light source, why does the current increase as you decrease the retarding potential, below the stopping potential. Isn't the ...
2
votes
0answers
86 views

Are new discoveries in quantum physics (e.g. Amplituhedron) supporting one of the classical QM interpretations? [closed]

Are new discoveries in quantum physics (e.g. Amplituhedron, Higgs boson) supporting one of the classical QM interpretations? For example Copenhagen, Everett many worlds or Penrose interpretations. Or ...
0
votes
1answer
60 views

Intuitive way to think about discrete energy levels

I'm currently taking an introductory quantum mechanics course and we just finished learning about the infinite square square well scenario. I understand all the maths used for calculating the ...
1
vote
1answer
216 views

Explain confinement energy for a particle in a box

What is a "particle in a box"? How does confinement energy equal kinetic energy? How does confinement energy relate to the spectrum energy (the absortion/emission between energy)?
2
votes
0answers
53 views

Condition for CP violation

I am studying how weak and strong phases lead to CP violation. I am following CP Violation by Branco. There is some algebra that I can not follow. Consider the process : $ a + \bar{a} \rightarrow b ...
2
votes
4answers
423 views

Clarification about Wave-particle duality

Okay,so I am learning about the double slit experiment done with electrons. I saw this picture, which shows the interference pattern being built up slowly with increasing number of electrons: I ...
1
vote
0answers
103 views

Derivation of Schrodinger equation using unitary operators

I encountered the derivation of Schrodinger time dependent equation using expansion of a unitary time propagation operator into power series in a small quantity $\delta t$, working to first order in $\...
1
vote
2answers
85 views

Energy in an infinite potential well in one dimension

We consider a particle in an infinite potential well in one dimension. The particle is describe by the arbitrary wave function $\psi(x)$. For our particle, we have to show that: \begin{...
3
votes
1answer
179 views

Relationship of symplectic group (Hamiltonian structure) to unitary group in quantum mechanics?

Wikipedia claims here that the 2 out of 3 property is the following relationship between unitary, orthogonal, symplectic, and general linear complex groups: $U(n)=Sp(2n,R)∩O(2n)∩GL(n,C)$ Intuitively ...
0
votes
1answer
88 views

Will dynamo generate electricity with reverse spin?

Will a dynamo generate electricity when it is spinning in opposite direction? If we alternate the rotation direction every minute, will it still generate electricity? How?
2
votes
1answer
54 views

Operator difference $\frac{d}{dx}$ and $d_x$ in quantum mechanics

In Dirac's book there is a displacement operator, $d_x$, which I conceived to be the same as derivative operator. But apparently it is not. What is the difference? They lead to different relations to ...
-1
votes
1answer
124 views

Do Quantum Mechanics At The Macro Scale Disprove General Relativity or Prove Something New?

We all know about the discrepancy between relativity and quantum physics at the scale relative to particles. Wouldn't the fact that recent experiments show quantum effects at the macro-scale in some ...
3
votes
0answers
53 views

Magnetic dipole moment of $^3$Li$^7$ nucleus

In a quantum book I am reading for self-study it is noted that the magnetic dipole moment of the $^3$Li$^7$ nucleus can be calculated as $\mu = 1.67 \times 10^{-26} J\cdot T^{-1}.$ However there is ...
2
votes
2answers
81 views

Why can't be the EPR experiment simplified?

Alice measures the spin of her electron on the x axis. She now knows the spin value of Bob's electron on the x axis at time T0. Bob measures the spin of his electron on the z axis. He now knows the ...
1
vote
1answer
104 views

Total quantum dimension of excitations in the Toric code

In the Toric code, the excitations are e, m, fermion $\epsilon$ and vacuum. Thus, the total quantum dimension is $D= \sqrt{\sum{d_{a}^{2}}} = 2$. It seems one takes into account all sorts of possible ...
0
votes
1answer
124 views

What did Feynman mean by 'energy shift' here?

I was reading Feynman's Lectures III's Chapter 10: Other Two-State Systems. There he discussed about hydrogen molecular ion having two base states: The amplitude of the molecule to go from $|1\...
0
votes
1answer
183 views

Transformation of operator matrix under change of basis [duplicate]

How does operator matrix transform under change of basis? If $\rvert \beta\rangle$ and $\rvert \alpha \rangle$ are two bases related by transformation $ \rvert\beta_m\rangle = \sum_n S_{mn} \rvert\...
8
votes
2answers
517 views

How to derive the theory of quantum mechanics from quantum field theory

I have read the book on quantum field theory for some time, but I still do not get the physics underline those tedious calculations. The thing confused me most is how quantum mechanics relates to ...
1
vote
2answers
235 views

Does the following experiment disprove the Copenhagen interpretation?

I have a question concerning the scientific experiment proposed in the following video, (25:00-29:00) titled the "EPR Thought Experiment", which bears resemblance to the quantum eraser experiment. ...