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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Gauge Invariance of the Hamiltonian of the electromagnetic field

The Hamiltonian for an electron of mass $m$ and charge $e$ in an exterior electromagnetic field is $$H=\frac{1}{2m}(p-(e/c)A)^2+e\varphi.$$ The corresponding (via canonical quantization) quantum ...
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2answers
66 views

What is a degenerate Fermi gas?

In ultracold atoms, it is generally talked of a degenerate Fermi gas. What does degenerate mean here?
0
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0answers
51 views

Beta-decay of the neutron

Could you please tell me, where can I find a straightforward calculation with all details of beta-decay of neutron? To find the amplitude and to square it is difficult, but possible. The main problem ...
8
votes
3answers
284 views

Is the Copenhagen interpretation merely an approximation to quantum mechanics?

So, I'm reading Max Tegmark's Our Mathematical Universe (Knopf edition, p. 229). He's discussing Everett/MWI for a bit and I'm not really paying attention and then I wake up to this: [I]t's time ...
1
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0answers
122 views

Basic introductory quantum mechanics question [closed]

Given that $\psi = \frac{1}{\sqrt{32 \pi a_{0}^{3}}}(2-\frac{r}{a_0})exp(\frac{-r}{2a_0})$ is a wavefunction of the hydrogen atom, write down the probability density for r and calculate the ratio ...
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0answers
71 views

Proofs on Quantum Inequalities?

Are there any experimental proofs witch support The Quantum inequalities and The Quantum interest conjecture?
2
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1answer
276 views

Are all spin states orthogonal?

For a spin 1/2 particle you have two spin states, either up or down which are orthogonal. But what about a spin 1 particle which has 3 spin states, either up, down, not up/not down?
1
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1answer
76 views

Eigenvalues of the Spin Operator on a two-spin-system

I am not sure if I understand spin operators correctly. Given a two spin system in state $|++\rangle$ and an operator $S = S^{(1)} + S^{(2)}$ Then I have $$ S_z |++\rangle = (S^{(1)}_z + S^{(2)}_z) ...
0
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1answer
254 views

Proof of the time-independent Schrödinger equation

I have a question regarding the proof of the time-independent Schrödinger equation. So if we have a time-Independent Hamiltonian, we can solve the Schrödinger equation by adopting separation of ...
1
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1answer
120 views

Regarding state of Klein-Gordon field

In regular quantum mechanics of particles, I have the Schrodinger evolution picture for a general state $$ i\hbar \frac{d}{dt} \left|\psi(t)\right> = \hat H \left|\psi(t)\right> $$ then we ...
0
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1answer
56 views

Square of the momentum operator (issue with taking dot product of complex numbers)

So the momentum operator in coordinate space is: $$ \vec{p} = -i\hbar\vec{\nabla}$$ And the hamiltonian for a free particle is: $$ H = \frac{p^2}{2m}$$ All over the internet I see this written as: $$ ...
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2answers
124 views

Dealing with dirac notation with regards to different basis'

So this should be a pretty simple question. So we say that $\langle x | \psi \rangle = \psi(x)$. In other words $\psi(x)$ is the ket $|\psi\rangle$ expressed in terms of the $x$ basis. Now suppose ...
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2answers
381 views

Normalization of Momentum Eigenfunctions: the number of particles

After finding the eigenfunctions $u_p(x)=Ce^{ipx/\hbar}$ of the momentum operator just like in this UCSD lecture notes, one seeks to normalize them, so one first tries: ...
2
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0answers
57 views

What is the difference between Lehmann-Kallen and Dispersion relation?

I know that the Lehmann-Kallen (LK) form of an operator concerns just that, an operator. But the LK is very similar in form to dispersion relations found in analytic S-matrix theory.
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1answer
149 views

Expectation values in QFT?

What is the meaning of different expectation values in QFT? For instance: $$\langle 0|{\cal O}(0)|q,s\rangle$$ or $$\langle 0|{\cal O}(0)|0\rangle$$ with ${\cal O}$ being some operator and ...
2
votes
1answer
157 views

Spin state of electron after measurement

I have a system of two spin 1/2 particles in a superposition of spin states in the z-direction given by: $\psi = \frac{1}{2} |+ +\rangle + \frac{1}{2} |+ -\rangle + \frac{1}{\sqrt{2}} |- -\rangle$ ...
3
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1answer
254 views

Time-ordered operator in Srednicki

On page 51 Srednicki states, "Note that the operators are in time order...we can insert $T$ without changing anything". This I agree with. But then on the next paragraph he states "The time order ...
3
votes
2answers
286 views

Second order energies of a quartic pertubation of a harmonic oscillator

A homework exercise was to calculate the second order perturbation of a a quantum anharmonic oscillator with the potential $$ V(x) = \frac{1}{2}x^2 + \lambda x^4 $$ We set $\hbar = 1$, $m=1$, etc. ...
0
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1answer
133 views

Quantum state with zero standard deviation of position operator

Is any quantum state $|\psi\rangle$ possible such that the standard deviation $\sqrt{\langle\psi|(\Delta\hat{x})^2|\psi\rangle}$ of the position operator $\hat{x}$ is zero? If not, why?
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1answer
82 views

What do they mean with: photon scattering with $q^2=-Q^2\leq 0$

In a scattering problem, let q denote the four-momentum of the photon. Is $q^2=-Q^2\leq 0$ simply a statement of what metric one uses and simultaneously a definition of $Q^2$?
-5
votes
1answer
142 views

Collapse in Quantum Field Theory? [duplicate]

I do not want answers telling me that wave-function collapse is not real and decoherence is the answer (I know the situation with that). I am asking a question purely on the basis if wave-function ...
-2
votes
1answer
76 views

Does alternative reality theoretically prove? [closed]

Does Hugh Evert theory means Alternative-Reality (or in general, Parallel-Worlds) and Many-Worlds-Interpretation theoretically prove? Or are scientists have any progress to prove it?
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1answer
122 views

Why photon-electron energy transfer can't occur in steps or does it?

The process of exchange of energy between a photon and an electron only occur after a specific energy called work-function of the material. Thus, the energy transferred is quantised due to the fact ...
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2answers
79 views

What causes different decays?

Nuclei spontaneously decay according to a certain decay rate. There are however different kinds of decay, alpha, beta, gamma... What causes then the nuclei, when they decay, to do so in one way of ...
2
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1answer
83 views

Uncertainty on a single observable measurement

Heisenberg Uncertainty Principle states (in the form of the Robertson-Schroedinger Formula) that measurement of two non-commuting observables has a limiting precision, even for flawless measurement ...
2
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1answer
57 views

Can there exist a Wave which changes the quantum states of particles?

i'm a high school student and i was reading about electromagnetic waves and how they transport energy and that the electric and magnetic fields sustain each other. I have also read about longitudinal ...
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0answers
37 views

Flammability and statistical mechanics

I am wondering to what extent the flammability can be predicted from the statistical properties of an ensemble. Given the partition function of an ensemble, can we in principle predict this property? ...
3
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1answer
165 views

TISE for a triangular potential

I want to solve the TISE of a particle of charge $q$ and mass $m$ in a one dimensional triangular potential, with an infinitely high potential wall at $x = 0$, i.e. ...
0
votes
0answers
48 views

Length of orbit on Bloch sphere

I'm not sure whether this question is well defined, but I am interested in the volume of the (obviously not linear) subspace of qubits $$ \left|\Psi\right\rangle = \alpha \left|\uparrow\right\rangle + ...
5
votes
1answer
441 views

Matrix representation angular momentum

We are supposed to give a matrix representation of $L\cdot S$ for an electron with $l=1$ and $s=\frac{1}{2}$. I read $L\cdot S$ as $L \otimes S$. Is this correct? Then we would have e.g. for ...
1
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1answer
95 views

Angular momentum and spin

I am having problems with this excercise. We look at a system where the total angular momentum is given by an electron with $l=1$ and $s=\frac{1}{2}$. Now I am supposed to calculate the ...
3
votes
0answers
60 views

Thermalising a sub-system of a larger, interacting system

I'm considering a joint system consisting of a spin-1/2 particle (qubit) and a spin-l particle (reference) coupled via a Hamiltonian $H_0$. At a certain point I want to couple the qubit to a bosonic ...
0
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1answer
152 views

Is there a way of measuring the spin along an arbitrary direction of a spin 1 particle?

I am familiar with the expression for spin 1/2 but haven't seen one for spin 1.
0
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0answers
45 views

Collapse of wave function

Can the collapse of a quantum mechanical state in general into one the eigenstates of an observable whenever its measurement is made written mathematically? If yes, how?
5
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5answers
450 views

Does a photon instantaneously gain $c$ speed when emitted from an electron?

An excited electron looses energy in the form of radiations. The radiation constitutes photons which move at a speed $c$. But, is the process of conversion of the energy of the electron into the ...
2
votes
3answers
472 views

Commuting momentum and position operators?

I think this is a question about the mathematical axioms of quantum mechanics... Consider the following operators $\tilde{x}$ and $\tilde{p}$ on Hilbert space $L^2(R)$, defined for fixed ...
0
votes
1answer
281 views

Overview and doubts about Bloch's theorem and the concept of partial density of states

So I have a large confusion with QM as applied to solid state. The following is a summary of what I know, what I think I know, and what I know I don't know. I hope to stir a discussion that will help ...
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2answers
263 views

Possible spin states?

Given a system of two particles with spin up and down, I have troubles to understand the possible states of this system. I would have normally thought, that the possible states are the tensor ...
3
votes
1answer
137 views

What is the Weyl algebra of a confined bosonic particle?

The abstract Weyl Algebra $W_n$ is the *-algebra generated by a family of elements $U(u),V(v)$ with $u,v\in\mathbb{R}^n$ such that (Weyl relations) $$U(u)V(v)=V(v)U(u)e^{i u\cdot v}\ \ Commutation\ ...
0
votes
1answer
222 views

Should I learn Classical Physics if I want to learn Quantum Physics? [duplicate]

I don't remember anything from school, so please what do you say about the title?
3
votes
1answer
1k views

Change of basis in Dirac Notation

Question: An operator $A$ is in a particular basis $|a_i\rangle$ (where $i=1,2$), and is represented by $$A=\begin{pmatrix} 0 & -i \\ i &0 ...
2
votes
2answers
442 views

Solving quantum radial equation for infinite potential spherical annulus for $l=0$

There is a mass $m$ in a potential such that $$ V(r) = \left\{ \begin{array}{lr} 0, & a \leq r \leq b\\ \infty, & \text{everywhere else} \end{array} \right. $$ ...
6
votes
2answers
182 views

No non-trivial UV asymptotically free and IR free

How it could be proven that a non-trivial theory cannot be both asymptotically free and IR free (g=0 both in the UV and IR with some interpolating function in between)? This is of course contrary to ...
0
votes
0answers
78 views

Double-slit experiment formulated in a quantum circuit

What would the double-slit experiment or something analogous to it look like implemented as a quantum circuit/program? Also, what about the delayed choice quantum eraser, how would that look in a ...
2
votes
1answer
113 views

Quantum fluctuations in a classical domain?

"In the presence of chaos, even small fluctuations (including quantum fluctuations) can be amplified to produce large uncertainties in later behavior"(http://arxiv.org/pdf/gr-qc/9210010v2.pdf) Is there ...
13
votes
4answers
556 views

How is it possible that quantum phenomenons (e.g. superposition) are possible when all quantum particles are being constantly observed?

I don't understand how quantum mechanics (and therefore also quantum computers) can work given that while we work with quantum states, particles that this quantum state consist of cannot be observed, ...
2
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0answers
85 views

Geometric quantization in Kepler problem in hydrogen atom

Why in the usual geometric quantization calculation the dimensions of eigenspaces is wrong (we can see this obstacle for Kepler problem in hydrogen atom). Here is a refference see
3
votes
1answer
168 views

Transmission + Reflection coefficients >1 For Potencial Barrier with Negative Complex Part Contradicts Paper

I am studying reflection and transmission coefficients for a barrier consisting of a a step potencial defined by: $$V(x):=\begin{cases}0&{\rm if}\,|x|>a/2 \\ V_0+iW_0 & {\rm ...
2
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1answer
123 views

Is boson sampling a problem in 'continuous variable' quantum information?

When people generally speak of quantum information in the context of continuous variables, what is generally meant is that observables, like position/momentum or the field quadratures of quantum ...
2
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2answers
215 views

What is the reason for the electrons in a given subshell to orient in certain preferred regions?

My text book says: "Magnetic quantum number describes the behavior of electron in a magnetic field. We know that the movement of electrical charge is always associated with magnetic field. Since ...