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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Do the norms of the total and the orbital angular momentums commute? If yes, why is there a problem with 2p_{1/2}?

Question: For $\vec L$ the orbital angular momentum of an electron, $\bar S$ its spin, and $\vec J:=\vec L+\vec S$ the sum, do $\vec J^2$ and $\vec L^2$ commute? I assume it does: $[\vec J^2,\vec ...
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2answers
66 views

Is there any gravitational force between two stationary neutrinos, a billion light years apart?

Gravity is supposed to act over an infinite distance. But if the force is very weak (due to low masses) and the distance is very far, is the force actually 0? Or is the force so low that it is ...
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2answers
36 views

How many photons are absorbed during Rabi oscillations?

In my understanding, Rabi oscillations are derived using the classical approximation for the electromagnetic field. I don't get how this picture fits with a quantized EM field though. Say you excite a ...
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1answer
47 views

Commutator between square position and square momentum [duplicate]

I need (as a part of one exercise) to find commutator between $\hat{x}^2$ and $\hat{p}^2$ and my derivation goes as follows: $$[\hat{x}^2,\hat{p}^2]\psi = [\hat{x}^2\hat{p}^2 - ...
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2answers
49 views

How to use Hartree-Fock for helium?

I am thinking of using Hartree-Fock approximation to calculate the ground state energy of helium. The ground state wave function must have a symmetric orbital wave function. But in HF we need a Slater ...
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1answer
85 views

Immortality within the multiple worlds interpretation of quantum mechanics [closed]

I understand the multiple worlds interpretation of quantum mechanics as follows: Any time an event happens, all of the possible outcomes take place ("split the universe") If I then think about a ...
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2answers
34 views

Quantum measurement problem with eigenvectors (Dirac notation) [closed]

Ok so I've got two state vectors related to two other state vectors. $$|\alpha_1\rangle= (1/5)(3|\gamma_1\rangle+4|\gamma_2\rangle)$$ $$|\alpha_2\rangle= (1/5)(4|\gamma_1\rangle-3|\gamma_2\rangle)$$ ...
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2answers
56 views

Looking for a simple example of generating unequal probabilities in QM

I am trying to understand the problem of branch counting in Everettian interpretations of QM, so I thought I would try to analyze a simple example of starting with equal branch amplitudes that evolve ...
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1answer
131 views

Why is time evolution unitary

Is the reason why the time evolution operator is unitary based on purely physical arguments, i.e. that the physical processes that an isolated system undergoes shouldn't depend on any particular ...
2
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2answers
59 views

What makes quantum decoherence different from dissipation?

From my understanding quantum decoherence and dissipation are completely different ways of modelling information loss to the environment. Dissipation can be modeled using the Caldeira-Leggett model ...
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1answer
53 views

Energy levels in close-proximity of each other in time-independent degenerate perturbation theory

I've applied second order time-independent degenerate perturbation theory corrections to the energy with the method presented in Modern Quantum Mechanics by J.J. Sakurai. I shortly summaries this ...
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1answer
36 views

Definition of quantum microcanonical ensemble in Landau&Lifshitz

I'm reading the first chapters of Landau&Lifshitz 's [Statistical Physics][1] and I don't understand the definition of the quantum microcanonical ensemble. The microcanonical distribution for a ...
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1answer
66 views

What is the Meaning of the equation $\frac{d\sigma}{d\Omega}=\left|f(\theta,\phi)\right|^2$

In the "Preface for Students" of the book "Quantum Field Theory" by Mark Srednicki is a set of equations. Quoting from the author: "In order to be prepared to undertake the study of quantum field ...
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1answer
60 views

Group Theory VS Quantum Mechanics [closed]

We all know that a quantum state or an observable, for example $|\phi>$ is a vector in Hilbert space. What is the equivalent of a quantum state (or simply a state) in group theory?
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2answers
84 views

Why is the “complete metric space” property of Hilbert spaces needed in quantum mechanics?

I have been learning more about Hilbert spaces in an effort to better understand quantum mechanics. Most of the properties of Hilbert spaces seem useful (e.g. vector space, inner product, complex ...
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2answers
31 views

Interaction Hamiltonian in the interaction picutre

The Schrodinger and Heisenberg pictures make sense to me. But the interaction picture which is a hybrid of the two does not. Author of this text first splits the Hamiltonian up as ...
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1answer
101 views

Perspectives of QFT [on hold]

From the answer to this question Computing $\langle0|T[Q(t_2)Q(t_1)]|0\rangle$, I have discovered that there is two perspectives to QFT. I am doing a course which is unfortunately a summary of QFT and ...
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1answer
19 views

Spin Constancy During Transitions

If you impose an external B field, with components x, y, z given as (0,B,0), on a free electron, this may produce precession of the y spin axis and I generally follow the simple Hamilition structure ...
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3answers
525 views

Uncertainty principle and measurement

I would like to really understand how the uncertainty principle in QM works, from a practical point of view. So this is my narrative of how an experiment goes, and I'm quickly in trouble: we prepare ...
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1answer
33 views

What is quantum states of a gas? Is it the principle quantum no.?

When we write that the possible quantum states of a system are $S=1,2,3.\dots$, how is that related with the four quantum numbers, especially with the spin of a particle? Also according to BE ...
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2answers
43 views

Why does a plane wave leave the position of the particle unspecified?

I'm covering a book on QM, and just started recently and I'm stuck at understanding something. It says that we can describe the state of motion of a particle with an infinite plane wave equation: ...
4
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0answers
56 views

Feynman Path integrals in space with holes in it [closed]

Feynman Path Integrals are a way of calculating the wave function of quantum mechanics. It usually integrates every possible path through all of space. I wonder if there is any study of Feynman path ...
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2answers
76 views

Are physical constants determined by their observation?

In common interpretations of quantum mechanics, it can only be said that objects exist once I observe them - it is not legitimate to ask where an object was before I observed it. Does this point of ...
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1answer
45 views

Finite time involved In electron transitions

From Wikipedia: "Atomic electron transition is a change of an electron from one quantum state to another within an atom. It appears discontinuous as the electron "jumps" from one energy level to ...
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2answers
49 views

Quantum fortune teller

A diffraction pattern in a double slit experiment only occurs if randomness is preserved for which way the photon goes and once certainty is determined by actual measuring the pattern is lost. Can ...
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1answer
42 views

Infinite halving of a distance

If an object is, say, 100 cm. from a wall, and I move the object halfway to the wall and stop, then the distance is reduced to 50 cm. If I continually move the object by one half of the remaining ...
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1answer
52 views

How do states in Hilbert Space act like irreducible representations?

I am reading Georgi's book on group theory and I came across this sentence..." Hilbert space of any parity invariant system can be decomposed into states that behave like irreducible representations". ...
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1answer
76 views

Writing down many particle Hamiltonian

We are given that \begin{align}\mathrm{tr} e^{-\frac{i}{\hbar}\hat{H}t}&= \int D[a_1,\dots,a_n]\times\\&\qquad\exp\left[\int_0^t dt' \left(\frac{1}{2}\sum_j ...
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1answer
53 views

Computing $\langle0|T[Q(t_2)Q(t_1)]|0\rangle$

Given Hamiltonian $H=\frac{P^2}{2}+\frac{\omega^2}{2}Q^2$, compute $\langle0|T[Q(t_2)Q(t_1)]|0\rangle$, where $T$ is the time-ordering of the product, $|0\rangle$ is the ground state. Now set ...
2
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3answers
151 views

Quantum Mechanincs - Dirac notation and solving time dependant schrodinger [closed]

The $\hat{S}_{x},\hat{S}_{y},\hat{S}_{z}$ obviously correlate to $x,y,z$ components of the operators. Consider the Hamiltonian: $$\hat{H}=C*(\vec{B} \cdot \vec{S})$$ where $C$ is a ...
2
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2answers
79 views

Heisenberg uncertainty and probabilistic nature of QM

I am trying to understand whether the HUP and the probabilistic nature of QM are orthogonal or not. By that I mean that the HUP fundamentally derives from operators not commuting, which is the ...
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0answers
35 views

What is quantum entanglement [duplicate]

I'm very confused with quantum entanglement. And I want to know can we make a machine using quantum entanglement to transfer data for far long distance like transferring data between mars to earth. ...
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1answer
56 views

Problem with momentum operator

Why is there no problem with the eigenfunction of the momentum operator being non-normalisable? How can it be a valid quantum state?
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35 views

RH side of the Uncertainty principle: when is it a number and when an expectation value?

The uncertainty principle between the position $x$ and the momentum $p$ is given by: $$ \sigma_x \sigma_p \geq \hbar/2,$$ whereas for the $x$ and $y$ components of the angular momentum is given by: ...
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2answers
98 views

Why do objects have size? [closed]

What is the reason objects, like coffee mugs, have size?
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2answers
204 views

Why are the spin operators defined as they are?

$$\begin{align*}S_z &= \frac{\hbar}{2} \left(\left|+\right>\left<+\right| - \left|-\right>\left<-\right|\right)\\ S_y &= i\frac{\hbar}{2} \left(\left|-\right>\left<+\right| - ...
12
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3answers
315 views

Is there a prediction of quantum mechanics that could be construed as representing an “energy-time uncertainty relation?” [duplicate]

As the title suggests. Is there a prediction of quantum mechanics that could be construed as representing an "energy-time uncertainty relation?" Does there exist any reference to such a prediction, or ...
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4answers
129 views

What does “spread of momentum” actually mean?

I was reading Feynman's lecture in which Feynman invoked his own way of explaining the uncertainty principle using single-slit experiment. There I found: To get a rough idea of the spread of ...
2
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1answer
67 views

Why does $tr \ e^{-\frac{i}{h}\hat{H}t}= \int d^nr \left< \textbf{r}| e^{-\frac{i}{h}\hat{H}t} | \textbf{r} \right>$ hold?

I would like to consider the trace of the time evolution operator $e^{-\frac{i}{\hbar}\hat{H}t}$ Apparently in single-particle quantum mechanics is can be represented as $$ tr \ ...
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0answers
25 views

Does the shell structure really make sense for a high-Z atom?

The shell structure picture is based on the mean field approximation, which replaces the interaction between the electrons by some mean-field potential. For a high-Z atom, like Fe, or even Ur, is the ...
5
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2answers
359 views

Does the $\frac12mv^2$ law apply to quantum mechanics?

Consider the classical Hamiltonian for a spring: \begin{equation} H = \frac{1}{2}\frac{p^2}{m} + \frac{1}{2}kx^2 \end{equation} This is one of those simple cases where when you work out the math we ...
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2answers
134 views

How can I prove following density matrices have same eigenvalues?

I have the following two density operators, the paper I am reading says that these two operators have same eigenvalues $$\rho^i = \frac{1}{3} ( |0\rangle \langle 0 | +|1\rangle \langle 1 |+|2\rangle ...
2
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1answer
35 views

Product on Tensor Products

I'm trying to understand how products on tensor products work. For instance, in quantum mechanics, you have ($x$ tensor $y$) times ($z$ tensor $a$), where $x$, $y$, $z$, $a$ are all operators acting ...
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2answers
48 views

Is lightning an example of energy emision from accelerated charge?

I have always heard that the inconsistency in explaining atomic models with classical mechanics was that the study of electrical charges had shown that whenever a charge is accelerated, it emits light ...
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2answers
80 views

multiverse fabric of reality

Source-"fabric of reality"- author d. deutsch - his contention, as I understand it, is that quantum interference is caused by "almost, but not identical quite quantum entities" , e.g. electrons, from ...
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1answer
71 views

What are the consequences of ignoring non-physical solutions?

a particle in a finite width 1 - D quantum well, produces 2 math solutions outside the well walls ( $e^{bx}$ and $e^{-bx}$,( ignoring normalising factors.) The decaying function, $e^{-bx}$, is used ...
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1answer
85 views

How much information does the Hamiltonian contain in quantum mechanics? [closed]

Given a Hamiltonian, let's say of a many-body system, through the Schrodinger equation,in principle we can find the eigenfunctions and their corresponding eigenvalues (spectrum). Now given an ...
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2answers
96 views

Why we cannot describe operator for force $F$ in quantum mechanics?

In quantum mechanics we describe operators corresponding to momentum but we don't define operator for force what is the reason behind it?
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141 views

Why are neutron absorption cross sections high at low incident energy?

For example, U-235 fission cross section looks like this: As I understand it, the resonances peaks correspond to discrete quantum states of the excited compound nucleus. As you go higher, the ...
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34 views

Problems and applications of Topoligcal Insulators today [closed]

I am learning about topological insulators in my applications of quantum mechanics class and i was wondering why exactly are they important? Who cares if the material only conducts on the surface? ...