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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1answer
30 views

Can hydrogen atom state be a superposition of 2 pure states with opposite spin?

The task is: We are performing measurements on hydrogen atom, that is in an unknown state $\psi$. $\psi$ is a superposition of $n=1$ and $n=2$ pure states and is orthogonal to ...
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0answers
19 views

Mutiplication properties about trace of two operators

Consider two operators $A$ and $B$, their functions $e^A$ and $e^B$ and a basis that mutual diagonalizes $A$ and $B$. Can I say that $Tr\left[e^Ae^B\right]=Tr\left[e^A\right]Tr\left[e^B\right]$? If ...
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0answers
11 views

Does point group symmetry also act within “spin space” for a lattice spin system?

As an example, let's consider a quantum spin system on a 2D square lattice. The lattice point group symmetries include $C_4$ rotation, parities, etc.... And let's take $C_2$ symmetry (2-fold rotation) ...
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0answers
7 views

Nearest Neighbour Spacing Distribution - Quantum chaos

it's always mentioned that the NNS of a "regular" quantum system follows a Poisson distribution. But when I have a look at this picture: for example when I look at F=500V/cm, where I'm in the ...
4
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1answer
64 views

Is the expression $S=K \log(\Psi)$ appearing in Schrödinger's first paper well defined?

I am currently reading Schrödinger's papers and happen to have some questions that maybe some expert in the field could clarify for me. Like what happens with $$S = K \log(\Psi)$$ when $\Psi<0$. ...
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1answer
41 views

Tensor operators and transformation of $O^s_l|j,m,\alpha\rangle$

In H. Georgi's Lie Algebras etc one defines a tensor operator transforming under the spin-$s$ representation of $SU(2)$ as the set of operators $O^s_l$ (for $l=-s...s$) such that $$[J_a,O^s_l] = ...
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1answer
60 views

What is the relation between the half-time and the line-width of a radioactive nucleus?

Are they inversely proportional to each other? This is the case for the atoms, I think. The problem is that, for those isotopes like uranium 238, the half-time is as long as 4.4 billion years, and ...
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1answer
51 views

Why are transition amplitudes more fundamental than probabilities in quantum mechanics? [duplicate]

I am reading Quantum Theory: Concepts and Methods by Asher Peres. Terminology used in the book: $P_{\mu m}$ are "transition probabilities". They are the squares of "transition amplitudes". That is, ...
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1answer
26 views

Bohr Sommerfeld quantization

Why does the Bohr-Sommerfeld rule for quantization give the exact energy levels for a Simple Harmonic Oscillator?
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0answers
52 views

Non Hermitian Quantum Mechanics

I was just reading about Non-Hermitian Quantum Mechanics dealing with Hamiltonians $H$ that are not Hermitian operators. Then it is unclear that we get orthonormal eigenstates. Now, I was reading a ...
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2answers
39 views

Tensor product of two different Pauli matrices $\sigma_2\otimes\eta_1 $

I'm solving problem 3.D in H. Georgi Lie Algebra etc for fun where one is to compute the matrix elements of the direct product $\sigma_2\otimes\eta_1$ where $[\sigma_2]_{ij}\text{ and }[\eta_1]_{xy}$ ...
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3answers
53 views

$SO(3)$, $SU(2)$ and symmetries in quantum mechanics

A rotation in the vector space $\mathbb{R}^3$ is represented by the known 3x3-matrices. But at this point I'm really confused how to get from there to Quantum Mechanics. The group of ...
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0answers
33 views

How robin bird can understand the process of the Quantum biology?> [on hold]

In a Ted's Video named " Quantum Life: How Physics Can Revolutionise Biology: Jim Al-Khalili at TEDxSalford " The physicist provided an example of Quantum Biology at the 16th minutes that the bird ...
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0answers
26 views

Entanglement entropy vs entropy

I just read that if you have a pure density matrix state on a product space, then a way to define entropy in a subspace is to take the reduced density matrix state and define $S = 1- ...
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0answers
12 views

Transformation of the infinitessimal integration variable under a coordinate transformation [migrated]

I always get confused when I'm facing the 3D integral over space and have to do a coordinate transformation on the given function to solve the integral. Do some of you have tips/trick how to ...
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4answers
160 views

Are “uncertainties” in Heisenberg Uncertainity just standard deviations? [on hold]

Can someone confirm that the uncertainties in Heisenberg's uncertainty relation are really just standard deviations based on the expectation values? For example, the $\Delta x$ can be computed by ...
6
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2answers
50 views

Why must energy be increased in a cyclotron to refine measured distance?

I have been listening to Nima Arkani-Hamed's messenger lectures at Cornell, and was confused by one point. He says that in order to measure at increasingly small distances energy must be increased (he ...
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1answer
33 views

Unique characterization of tensor product state by map on fully separable states

Some article on quantum mechanics that I'm currently reading contains an unproved claim that I don't understand. I will explain it further below. Let $H_1$ and $H_2$ be Hilbert spaces, and let $S_1$ ...
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2answers
48 views

Is there enough information in a given quantum state to determine the state beforehand?

If I knew all the information about a state, and I knew the laws of physics in their complete totality, could I "reverse engineer" it to find, with 100% certainty, the state before it?
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0answers
39 views

Different kinds of trace for statistical ensembles

In the chapter 7 of the book "A Modern Course in Statiscal Physics" by L. Reichl, we found $Tr[\hat{\rho}]=1$ for microcanonical ensembles and $Tr_N[\hat{\rho}]=1$ for canonical and grandcanonical ...
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0answers
34 views

What changes the unitary evolution of particles when they decay? [on hold]

Imagine we have produced a Higgs boson in a $e^+e^-$ collision. This Higgs boson will travel until it decays in other particles. The outcomes are many, $e^+e^-$, $q\bar{q}$, $ZZ$... Every and each of ...
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0answers
43 views

Majorana zero mode and 1D Ising model

It is known that the one-dimensional (1D) Ising model can be mapped to a free Majorana model using a Jordan-Wigner transformation and its two degenerated ground states are well interpreted by the two ...
6
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3answers
505 views

Why is the Klein Gordon equation of second order in time?

I was wondering if there is any way to interpret the fact that the Klein Gordon equation is a 2nd order PDE in time. I mean, normally you would expect that as soon as you fix the initial wavefunction, ...
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0answers
19 views

Angles in Born approximation Spherical Potential

I have a question concerning (in my opinion) strange notation that arose in both the book by Shankar and Sakurai in the same manner. Where i am very confused by them both seemingly using the same name ...
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0answers
20 views

How to write down the Lippmann-Schwinger equation for such a problem? [on hold]

Suppose there are three particles, 1, 2, 3. Initially, particle 2 and particle 3 form a bound state. Particle 1 is free. Now we want to study the scattering of particle 1 against the 2-3 bound system. ...
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0answers
16 views

Commutative Observables Expressed as Functions of a Third Observable [on hold]

For my Quantum assignment, I have to prove that, if two observable operators A and B commute $\exists C $ s.t. A = f(C) and B=g(C) for some real-valued functions f and g. I'd appreciate any amount of ...
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2answers
86 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). ...
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1answer
26 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 ...
1
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1answer
47 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
67 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
78 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 ...
1
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0answers
27 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
103 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
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6answers
169 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
117 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 ...
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2answers
58 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
40 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 ...
6
votes
3answers
120 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 ...
4
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2answers
97 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 ...
0
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0answers
36 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 ...
2
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0answers
13 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
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2answers
33 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 ...
7
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1answer
92 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 = ...
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1answer
31 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
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4answers
673 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? ...
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0answers
20 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 ...