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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2answers
446 views

Lippmann-Schwinger Equation with Outgoing Solutions

I'm reading about Green's functions and how the Lippmann-Schwinger equation eventually leads to the textbook expression for the form of wavefunctions in the far radiation zone after scattering by a ...
1
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2answers
93 views

Why does most of the heat transferred on Earth come from the infrared part of the electromagnetic spectrum?

Why does the most of the heat transferred on Earth come from infrared part of electromagnetic spectrum?
1
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1answer
147 views

Obtain the eigenfunction of Jz for the wave function of an electron in a hydrogen atom? [closed]

The wave function of an electron in a hydrogen atom is given by Is this wave function an eigenfunction of Jz , the z-component of the electron’s total angular momentum? If yes, find the ...
5
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4answers
2k views

Complex conjugate of momentum operator

Consider momentum operator representation in position space. $$\hat{p}=-i\frac{\partial}{\partial x} \,\ \text{and its eigen functions are } e^{ipx} \,\text{and} \,\ e^{-ipx}.$$ $$\hat{p}e^{ipx}=pe^{...
2
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0answers
167 views

What are you studying when you study a Harmonic Oscillator in QM?

This probably is a naive question - so please forgive a self-studier. In the text I am studying, one builds a HO by placing a particle in a potential that increases quadratically from the origin. The ...
1
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1answer
264 views

Do generalized Pauli Operators generate SU(n)?

A commonly used generalization of Pauli Operators is the "clock" and "shift" operators summarized here: http://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices Pauli Operators are generators ...
11
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1answer
1k views

Why can't I use Bell's Theorem for faster than light communication?

I read this description of Bell's theorem. I understand he's restating it slightly, so there may be incorrect assumptions there, or I may have some. I think Bell's theorem should lead to FTL ...
2
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2answers
323 views

wave-particle duality and entanglement

By fundamental definition of a entangled system we can say that if we know the quantum state of one subsystem then we can describe the state of another subsystem. A particle possess wave-particle ...
0
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1answer
460 views

Infinite potential well with barrier in the middle- symmetric

So I'm having problems with the double infinite potential well given by $$V(x)= \left\{\begin{array}{ll} \infty & -\infty < x < -a-b \\ 0 & -a-b< x < -a \\ V_0 & -a < x <...
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0answers
342 views

Uncoupling a coupled oscillator Hamiltonian by change of variables

I'm working on the problem of two entangled harmonic oscillators with Hamiltonian: $$H = \frac{1}{2} [p_1^2 + p_2^2 + k_0(x_1^2 + x_2^2) + k_1(x_1 - x_2)^2].$$ Introducing the variables $x_± = \frac{...
2
votes
1answer
135 views

Expectation value of Hamiltonian in different pictures of quantum mechanics

We start with the familiar Schrodinger equation: $$ i\hbar \frac{\partial \left|\psi_S\right\rangle}{\partial t} = \hat{H}_S \left|\psi_S\right\rangle $$ As we switch to a different picture than ...
7
votes
2answers
679 views

When can we assume that the wavefunction is separable

While working out the stationary states of a single particle in a 3d infinite potential box ($V=0$ inside a cuboid of known dimensions, $V=\infty$ everywhere else), I realized I had to assume the ...
2
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0answers
239 views

How to calculate relative branching fractions of the $Z$ boson to specific pairs of “neutral lepton and anti-lepton”?

The PDG is listing values of "$Z$ couplings to neutral leptons" as $$ \begin{eqnarray} g^{\nu_{\ell}} & = & 0.5008 \, \pm \, 0.0008 \\ g^{\nu_{e}} & = & 0.53 \, \pm \, 0.09 \\ g^{\nu_{...
0
votes
0answers
71 views

How are the Lagrange equation and Feynmann path integral related? [duplicate]

My question is, where could I get some more info on how the Euler-Lagrange equations are related $$ \delta S [y(x)] =0 $$ with the Feynmann path integral formulation $ \int D[y(X)]e^{iS[y(x)]/\hbar} ...
6
votes
1answer
181 views

Will all physical quantities unchanged by this transformation?

I am reading an article about Bloch-Floquet state. My questions is in Part II.B and Appendix A of this paper, I will describe them below. The original Schordinger equation we consider is: $$i\hbar\...
4
votes
2answers
218 views

Why do we need non-trivial fibrations?

I am currently reading this paper. I understand how the Bloch sphere $S^2$ is presented as a geometric representation of the observables of a two-state system: $$ \alpha |0\rangle + \beta |1\rangle \...
1
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2answers
192 views

Is there any non-hermitian operator on Hilbert Space with all real eigenvalues?

The property of hermitian is the sufficient condition for eigenvalue being real. Is there any non-hermitian operator on Hilbert Space with all real eigenvalues? If there exist, then can all ...
1
vote
1answer
176 views

Why don't we need to normalize wavefunction to find probability distribution?

Consider an unormalized wavefunction of a rotor at $t = 0$, a combination of $n=0$ and $n=2$ states: $$\psi(\phi) = 3 - 2 \cos (2\phi).$$ Find the probability distribution in angle. The ...
2
votes
1answer
159 views

Dipole matrix elements through parity argument

I am trying to find the following dipole moment matrix element $(|n,\ell,m\rangle)$. $$e\langle1,0,0|\vec r|2,0,0\rangle$$ I believe that I can say this matrix element is zero because of parity. The ...
0
votes
1answer
91 views

Thermodynamic entropy vs. quantum mechanical entropy

Is there a fundamental difference in the definition of entropy when considering the classical thermodynamic picture vs. the quantum mechanical picture, or are they both fundamentally equivalent?
0
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3answers
490 views

Mass or no mass?

Do all forms of energy have a mass? We know by $E=mc^2$ that mass and energy are directly proportional, but there are massless forms of energy such as electro-magnetic waves. I am also told that there ...
3
votes
3answers
625 views

What does the Pauli Exclusion Principle say about a superposition of spin states?

Suppose we have an atom. It is commonly said that because of the PEP, two electrons can't be in the ground state unless they have opposite spins, because no two electrons can have the same ...
0
votes
1answer
5k views

Calculating the expectation value of a Hamiltonian

I want to calculate the expectation value of a Hamiltonian. I have a wave function that is $$\psi = \frac{1}{\sqrt{5}}(1\phi_1 + 2\phi_2).$$ I want to know if I set this up properly. The Hamiltonian ...
2
votes
2answers
237 views

Schroedinger equation. Why Potential energy instead of Force?

What is the reason Schroedinger equation is quoted in terms of potential energy instead of force?
4
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3answers
241 views

Can a wave possess spin?

Since a matter wave is associated with a particle in quantum mechanics, does the wave spins? I mean, can we visualize the spinning of wave or is it possible that the wave spins?
0
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1answer
75 views

Stern Gerlach Experiment

Since l=0 for a valence electron in 5s state of silver, L=0 and therefore magnetic dipole moment is also 0 which means that the beam should not have deflected at all. So, we introduced the property of ...
2
votes
1answer
115 views

Characteristic polynomial of a Matrix

In fact, this problem is more likely to be a math problem. When I read a paper(http://arxiv.org/abs/0707.2875), the author includes the characteristic polynomial for a type of matrix $A_k$ with ...
0
votes
1answer
86 views

First Order Time Depenent Perturbation theory of particle in magnetic field

So I am dealing with the following hamiltonian, and the following perturbation: $$H=-\mu B_0\sigma_z$$ $$V=\mu B_1(\cos(\omega t)\hat x-\sin(\omega t)\hat y)\cdot{\bf \sigma}$$ I am asked for the ...
2
votes
1answer
101 views

Why is $\vert I=1,I_3=1\rangle = -p\bar n$

My book doesn't explain well how to build a doublet of antiparticles that transforms the same way the particle doublet $(p,n)^T$ (proton neutron) does. They claim $$\tag 1 \vert I=1,I_3=1\rangle = -...
1
vote
1answer
230 views

How could there be a truly “pure” state?

If the Universe did start from a single point, then wouldn't all particles be fundamentally entangled? How then could there be a truly "pure" state?
11
votes
2answers
796 views

Quantum entaglement and the arrow of time

I have seen several claims to that quantum mechanics is required to explain the arrow of time which I take to mean the macroscopic irreversibility of physical systems. This is presumably to resolve ...
2
votes
0answers
260 views

Degeneracy, spherical harmonics

In a 3D oscillator, the energy levels are known to be $(n_x + n_y + n_z + \frac{3}{2})\hbar \omega = (n + \frac{3}{2})\hbar \omega$. Say for $n = 1$, any of the $n$'s can be $1$ and the rest are $0$. ...
2
votes
1answer
421 views

How do I simulate this simple quantum circuit in MATLAB

I want to simulate a circuit similar to the one below in MATLAB. If you have a state matrix describing the state of 3 qubits, I understand that you could apply a CNOT matrix tensored with and identity ...
3
votes
2answers
314 views

Understanding Well Defined States

I am self-studying from a text in QM. Well defined states are mentioned several times. By and large these are consistent and seem to be readily apparent: states of well defined energy are basis kets....
1
vote
1answer
84 views

Converting between (abstract) linear operators and their position representations

Just as we have an abstract state vector $|\psi\rangle$ and its position representation $\psi(\vec{x}) = \langle \vec{x} | \psi \rangle$, how do we transform between a linear operator, say $H$, that ...
3
votes
1answer
123 views

Off-diagonal terms of the Husimi $Q$ function?

The Husimi $Q$ function of a quantum state $\rho $ is defined as $ Q (\alpha)=\langle \alpha \vert \rho \vert \alpha \rangle $, where $\alpha = (x, p) $ is a phase space coordinate and $\vert \alpha \...
2
votes
1answer
219 views

Can “state” be considered a 5th dimension?

I searched for an answer to this question on Google but just found articles that mention either string theory or a 5th dimension in passing (such as Maxwell equations as they relate to Riemann ...
0
votes
1answer
98 views

A meaningful distinction between determinism and causality

Causality is generally accepted to be a fundamental physical principle. But quantum mechanics is acausal (e.g. there is no 'why' as to the result of a measurement of the position of a particle in an ...
3
votes
2answers
229 views

Quantum entanglement on cosmological scales

This may be a foolish question given my limited understanding of QM but here it is. As I understand quantum entanglement basically means that two particles evolve as a single "unit", i.e., are ...
6
votes
1answer
180 views

How can I simulate a model electronic hole?

Suppose I can solve time-dependent Schrödinger equation for several 1D particles (currently 3). I'd like to see, what an electronic hole is and how it behaves — in a series of numerical experiments. ...
1
vote
0answers
129 views

Ground state of spin in magnetic field

I am trying to solve a time dependent perturbation theory problem, and it involves the Hamiltonian $$H=-\mu B\sigma_z$$ And a perturbation $$V=-\mu B_1\sigma\cdot(\cos(\omega t)\hat x-\sin(\omega t)\...
11
votes
2answers
484 views

Why uncertainty principle is not like this?

In Griffiths' QM, he uses two inequalities (here numbered as $(1)$ and $(2)$) to prove the following general uncertainty principle: $$\sigma_A^2 \sigma_B^2\geq\left(\frac{1}{2i}\langle [\hat A ,\hat B]...
7
votes
1answer
307 views

Degenerate perturbation theory applied to topological degeneracy?

Consider a quantum system described by a gapped Hamiltonian $H_0$ with degenerate ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an ...
2
votes
0answers
64 views

When can I use semiclassical approximation?

I know that I can use semiclassical approximation for path integral approach (in quantum mechanics) $\int d[q]e^{iA}$ when action $A >>1 $. But how shall I use such condition? For example, ...
1
vote
1answer
137 views

Wave Function Integral I need help conceptually and Mathematically

$$\int_{-\infty}^{\infty}\frac{\partial^2\bar{\psi}}{\partial{x^2}}\frac{\partial\psi}{\partial{x}}~dx.$$ I have read that this is equal to Zero. Only problem is that what I am reading about doesn't ...
0
votes
1answer
1k views

Normalizing the sum of wavefunctions and calculating probabilty - understanding concepts

A state of a particle bounded by infinite potential walls at x=0 and x=L is described by a wave function $\psi = a\phi_1 + b\phi_2 $ where $\phi_i$ are the stationary states. So let's say we want to ...
2
votes
1answer
988 views

“Derivation” of the Heisenberg Uncertainty Principle

The question I outline below is my textbook's "derivation" of the Heisenberg Uncertainty Principle. The "derivation" my textbook uses involves wave packets. Suppose there are seven waves of ...
1
vote
1answer
175 views

Does the energy-time uncertainty principle require energy levels to have finite width?

The uncertainty principle also has the form: $\Delta$$E$$\Delta$$t>h/2\pi$ Now this should mean that the thickness of the lines we draw in the energy level diagrams to show energy change undergone ...
4
votes
2answers
358 views

The momentum of a hole

I'm currently working through "A Guide to Feynman Diagrams in the Many-Body Problem" by R.D. Mattuck (self study, not a homework problem) and am stumped by the following problem: "In a system of free ...
1
vote
2answers
225 views

Can we describe Quantum Mechanics using filters and matrices? [closed]

Can mathematical filters or ultrafilters be used to predict quantum physics 'events' as accurately as using matrices like Schrodinger did? Is there a way to explain some of the predictive power of ...