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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11 views

Is there a reason why the subset of our Hilbert space that corresponds to a particle is a vector subspace?

I'm trying to gain some intuition behind the definition that states a particle is an irreducible unitary representation of the restricted Poincare group (or more specifically, its double cover). ...
0
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0answers
32 views

energy levels in infinite square well paradox

The homework problem I have an one-dimensional infinite square well with length $l$ and a particle with mass $m$ in it. I'm also allowed to assume that the well is that small, speeds get ...
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0answers
9 views

Is the energy expectation value comparable to the equation from power series ansatz?

The Hamiltonian is given by $$ H = H_0 + \lambda H_1 $$ where $H_0$ is the unperturbed Hamiltonian, which solves the Schrödinger Equation $$ H_0 \left |n^{(0)} \right \rangle = E_n^{(0)} \left ...
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1answer
35 views

orbital angular momentum of the silver atom

In a silver atom, the first 46 electrons are all paired and according to David McIntyre in Quantum Mechanics, The electrons in the closed shells can be represented by a spherically symmetric cloud ...
2
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1answer
49 views

Are these two spin states the same?

Consider two sets of axes, $xyz$ and $x'y'z'$, and the two spin states \begin{align} |\psi\rangle &= A(|+_x\rangle + |+_y\rangle + |+_z\rangle)\\ |\psi'\rangle &= A(|+_{x'}\rangle + ...
3
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2answers
71 views

Basic quantum entanglement question [duplicate]

Please consider commenting on this basic quantum entanglement question or point me to articles that may enhance my knowledge. Does quantum entanglement only occur in pairs, or can three or more ...
0
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0answers
25 views

Exercise about Bethe Ansatz for $N=3$ particles on a ring of length $L$

Suppose there are $3$ bosons living on a 1-dimensional ring of length $L$. The Hamiltonian is given by $$H=-\sum_{i=1}^3\frac{\partial^2}{\partial x_i^2}+\sum_{1\leq j<k\leq ...
4
votes
2answers
88 views

Rectangular window $\psi$ wave-function and the calculus of $\langle p^2\rangle$ for it

I'm currently considering a rectangular window $\psi$ function: $$ \psi(x) = \begin{cases}\left(2a\right)^{-1/2}&\text{for } |x|<a \\ 0&\text{otherwise.} \end{cases} $$ I am interested in ...
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0answers
33 views

How differing height of original potential barrier leads to differing energy bands [on hold]

Question: How does differing the height of original potential barrier leads to differing energy bands. From my understanding, (and using the Kronig Penney potential model) lowering the potential ...
2
votes
6answers
159 views

Is $∣1 \rangle$ an abuse of notation?

In introductory quantum mechanics it is always said that $∣ \rangle$ is nothing but a notation. For example, we can denote the state $\vec \psi$ as $∣\psi \rangle$. In other words, the little arrow ...
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4answers
109 views

Why does the mathematical constant $e$ enter into quantum mechanics so much?

In A. Zee's book Quantum Field Theory in a Nutshell, he mentions on pages 11-12 the following formula which he assumes reader had encountered before: \begin{equation} \langle q | p \rangle ~=~ ...
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0answers
35 views

Does deBroglie relation describe all waves?

DeBroglie relation states that $p = h/\lambda$ and $E = h\nu$, and all waves can be characterized by $\lambda$ and $\nu$. Why do I keep hearing that this relation can only describe matter waves? A ...
0
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2answers
57 views

What is time evolution of probability density in quantum mechanics?

I was surprised to asked this on an exam. The reason being the probability density is described by $\psi^*\psi$ where $\psi$ assumes the form of ~ $cos(kx)exp(-iwt)$ and when we perform $\psi^*\psi$ ...
4
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0answers
35 views

Derivation of the Lippmann-Schwinger equation

I was trying to understand the derivation of the Lippmann-Schwinger equation in Sakurai's Modern Quantum Mechanics, Section 6.1. Our teacher presented a much simpler derivation, similar to that on ...
7
votes
3answers
117 views

Can someone explain Planck's constant simply? [on hold]

Can someone explain Planck's constant simply? I know the math, however I don't understand the relevance. To explain what I'm asking, what is the significance of it when doing quantum mechanical ...
3
votes
2answers
91 views

How can an inverted anharmonic potential $V(x)=-x^4$ have discrete bound states?

I've been watching the lectures on mathematical physics by Carl Bender on youtube where he uses the non-Hermitian Hamiltonian methods to prove that the inverted anharmonic potential $V(x)=-x^4$ has a ...
1
vote
0answers
32 views

If 2 photons collided head on, what would happen? [duplicate]

If 2 photons, in perfect synch (frequency, amplitude, etc. were all equal) and they collided head on, what would happen? Would they pass right through each other? Would they interfere, then go back to ...
1
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0answers
10 views

Simplification of matrix-element given the Wigner-Eckardt theorem and Clebsch-Gordon coefficients of a 1,1/2 system

How can I simplify the following matrix-elements $$\left\langle 1,1/2;m_1,m_2\left| S \right| 1,1/2;m_1^{'},m_2^{'} \right\rangle$$ given the Wigner-Eckard theorem $$\left\langle j,m|S|j^{'},m^{'} ...
2
votes
2answers
31 views

Magnetic Field and Flow of Vector Potential

I am sorry, when my question is not really concrete, but here we go. Consider the Hamiltonian function $$H(x, \xi) = \frac{1}{2m}\bigl|\xi - eA(x)\bigr|^2$$ corresponding to a charged particle in a ...
6
votes
0answers
61 views

How do you build a Lagrangian in particle/nuclear physics? (A specific example)

I know that the terms in the Lagrangian needs to be scalars (with respect to Lorentz symmetry etc.). Also I know that [see C. G. Tully (EPP) p. 85] in general, for $\psi$ in the fundamental ...
0
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1answer
64 views

What's the meaning of the propagator in QM?

Yesterday I was solving some exercises, and after solving the time evolution I was asked to find the probability of the system to some state. In specific: $$|\Psi(t)\rangle = ...
0
votes
1answer
27 views

In the stern-Gerlach experiement how do we know that the magnets don't change orientation of the electrons to up or down?

I watched this video: https://www.youtube.com/watch?v=rg4Fnag4V-E Say the electron's north pole started off 60 degrees from the south pole, since the electron has little mass wouldn't that make it ...
4
votes
4answers
660 views

Does bra-ket always assume all space?

One thing I never understood about the bracket notation is the limits of the inner product. Given $ \langle \psi∣\psi \rangle$, what can I say about the limits of integration of the inner product? ...
0
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0answers
18 views

Derivation of the Klein-Gordon equation from Schrodinger equation [on hold]

Can someone demonstrate how to transform the one dimensional Schrodinger equation, $$-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2}\phi = i\hbar\frac{\partial}{\partial t}\phi$$ into ...
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0answers
24 views

What is the difference between photon and phonon? [on hold]

In quantum mechanics, I have read about photons. The photons are the light particles, which has no mass. and it has energy. photons travels with the velocity of light. on the other hand I have heard ...
0
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0answers
12 views

How to infer the wave function $\psi$ of a EM wave?

There was a claim I read somewhere that said the wave function $\psi$ of a EM wave is measurable via $\vec E$ and $\vec H$ Can someone show how this works?
0
votes
1answer
31 views

Is anything without mass an EM wave?

For the longest time I thought the distinction between matter wave and other types of wave is the non-relativist mass of the "thing" under discussion. Photons are EM wave, electrons are matter waves. ...
0
votes
1answer
64 views

Why do particles have spins such as $1/2$, $3/2$, $5/2$? [duplicate]

What does it mean to have 'half' spin? I have looked on Wikipedia and a few youtube videos on spin but they don't explain what it means to have $1/2$ spin. I am 18 and only starting to learning about ...
0
votes
1answer
29 views

Trouble getting the matrix representation of a 4-state Hamiltonian

$\newcommand{\bra}[1]{\left\langle #1 \right|} \newcommand{\ket}[1]{\left| #1 \right\rangle}$I have a simple 4-state Hamiltonian and am trying to find the matrix representation (in order to determine ...
4
votes
0answers
59 views

Group theory and quantum optics

This is a question about application of group theory to physics. The starting point is the group $SU(n)$. I have a representation $R$ of $SU(n)$ that takes values on the unitary group on an infinite ...
2
votes
1answer
58 views

Deutsch's Algorithm. Unitary Transform $U_f$

I'm studying Deutsch's algorithm and I keep coming across the phrase along the lines of "There is a unitary transform (a sequence of quantum gates) $U_f$ that transforms the state $|x\rangle |y\rangle ...
0
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0answers
36 views

General two state system with general pertubation

I am trying to solve this two-level system with time independent perturbation problem Consider an atomic system with only two stationary states $|1\rangle$ and $|2\rangle$ , of respective energies ...
1
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0answers
44 views

Does Clairaut's Theorem apply to the Wave Function?

In Griffiths Intro to Quantum Mechanics, I came across a problem that asks the student to prove one of the consequences of the Ehrenfest theorem: $$\frac{d \langle p \rangle}{dt} = \left\langle - ...
2
votes
3answers
59 views

Classical Limit of the Quantum Harmonic Oscillator

The classical harmonic oscillator obeys an arcsine law in that the distribution of positions of the particle over a single time cycle is proportional to $\frac{1}{\sqrt{A^2-x^2}}$, $A$ being the ...
0
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1answer
29 views

In Bohmian mechanics, how does the particle's position affect where a particle is detected?

In Bohmian mechanics / pilot wave theory / de Broglie–Bohm theory, my understanding is that a particle's trajectory evolves based on its wave function, and that the position that particle is detected ...
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votes
0answers
46 views

Do all subatomic particles create interference patterns in the double slit experiment?

I thought it was only photons that did this but someone in the comments claimed protons and electrons could too.
1
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3answers
72 views

Calculation of $\langle p\rangle$ and $\langle p^2\rangle$ for wave function [on hold]

Given the wave function $$\psi(x)=A\exp\left[-a \left(\frac{mx^{2}}{\hbar}+it\right)\right]$$ I would like to calculate $\sigma_{p}$. \begin{align}\langle p\rangle &=\int ...
0
votes
3answers
61 views

What evidence is there for quantum leaps?

I find this very strange that an electron can 'teleport' from one energy level to another. So what evidence suggests this?
1
vote
2answers
62 views

Bra-ket of products

I was trying to solve the following problem. (Lifted from Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory by Szabo and Ostlund) I came across across a solution for ...
1
vote
1answer
49 views

Would quantum computers be better at everything a GPU normally does? [on hold]

I have a very basic understanding of what GPU's and quantum computers are good at. To me, it seems like they overlap, but maybe this isn't completely true. GPU's are good for graphics which requires a ...
2
votes
0answers
57 views

Understanding Tensor Product

Consider the operator $$e^{-i \hat{H} t/\hbar} = e^{-i (\hat{P} \otimes \hat{X}) t/\hbar},$$ where $\hat{X}$ and $\hat{P}$ are position and momentum operator of two different systems. We know that the ...
1
vote
2answers
72 views

How do particles interact in Bohmian mechanics / pilot wave theory / de Broglie–Bohm theory?

I've read that in the de Broglie–Bohm interpretation of QM, the particle directed by its wavefunction has a trajectory (meaning both position and velocity) and that these are the only properties ...
1
vote
2answers
158 views

Exotic quantum observables

Quantum physics inherited its physical quantities from classical mechanics (energy, momentum, etc). Each quantity is associated with Hermitian operator, but there seems to be a lot more Hermitian ...
3
votes
2answers
107 views

How do you determine the “phase” of a hydrogen eigenfunction?

I've been reading the wikipedia article on the atomic orbitals of hydrogen. They have a nice collection of diagrams, such as this one for n,l,m = 3,1,1 This is apparently showing the wavefunction, ...
0
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0answers
45 views

Question about derivations in Sakurai's Quantum mechanics, section 5.8 [duplicate]

If anyone is familiar with Sakurai's book, specifically section 5.8 on energy shift and decay width, I am stuck and could use some help. I can't see how he derives 5.8.9 (in the revised edition). He ...
1
vote
1answer
69 views

Sakurai QM section 5.8

If anyone is familiar with Sakurai's book, specifically section 5.8 on energy shift and decay width, I am stuck and could use some help. I can't see how he derives 5.8.9 (in the revised edition). He ...
0
votes
2answers
52 views

Why does the electron wave function collapse in a double slit experiment?

Did the electron wave function collapse in the double slit experiment due to being observed, OR is it that the electron wave function collapsed because the instrument used to measure it physically ...
3
votes
4answers
196 views

How can we prove that a photon is absorbed only once?

When I first heard about the photons and the double-slit experiment my immediate thought was the following: Alright, energy is not absorbed continuously but in discrete units, photons, but nature ...
0
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2answers
66 views

How does De Broglie–Bohm theory or pilot wave theory explain the results of the Stern–Gerlach experiment?

The Copehagen interpretation of QM explains the Stern–Gerlach experiment by asserting that a particle is in a superposition of states and doesn't have a definite spin until measured. However, the de ...
1
vote
2answers
46 views

How do we prove that two conjugate operators $X$ and $Y$ induce $\sigma_x$ and $\sigma_y$ driving terms when restricted to a two level subspace?

Suppose I have a Hamiltonian for a particle moving in a one dimensional potential $$H = H(X,Y) \qquad [X,Y] = i$$ where $X$ is the dimensionless position, $Y$ is the dimensionless momentum, and ...