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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3
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2answers
125 views
+150

What does the $I$-$V$ curve in josephson junction mean?

According to the $I$-$V$ curve for Josephson junction tunneling for S-I-S (superconductor-insulator-superconductor), Do we have any tunneling current for $0< V\leq V_c$? If yes, then why don't ...
1
vote
1answer
27 views

Dirac delta function definition in scattering theory

I'm studying scattering theory from Sakurai's book. In the first pages he gets to the following expression: $$\langle n|U_I(t, t_0)|i\rangle=\delta_{ni}-\frac{i}{\hbar}\langle ...
0
votes
0answers
10 views

Is wave-particle duality not clear from the single-slit experiment?

In experiments it is easy to discern between 2 and more-than-2 fringes on a screen, making the double-slit experiment the default one for wave-particle tests. Let's say we shoot massive particles ...
-1
votes
0answers
12 views

Speed of Electron delta orbital function [on hold]

Is there a function that determines the delta in speed of electrons in subsequent orbitals? If so, is it the same for all elements or does it differ because of relativistic effects? Would an electron ...
-3
votes
0answers
17 views

Gravity theory help? [on hold]

I'm looking for someone to help with math on a theory I have involving gravity on a quantum level. Anyone interested?
1
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0answers
31 views

Weyl's (and others') Unitary Basis

Galitski's Exploring Quantum Mechanics says (on p.29) 'the number of (linearly) independent unitary ($N$-dimensional) matirces is also $N^2$'. Since the set of unitary matrices does not form a vector ...
1
vote
1answer
175 views

Are the authors saying that the observer effect plays no role in Bohr's thought experiment of the Heisenberg uncertainty principle?

Here is an excerpt from Eisberg & Resnick's Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. Here is introducing Bohr's though experiment to establish a physical origin for the ...
0
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0answers
15 views

How to include Berry Connection in Hamiltonian?

When we calculate Berry connection, $A(R)=i<\psi(x,y)|\frac{d}{dR}|\psi(x,y)>\hat{R}$ corresponding to the Berry phase of any system, the gauge potential is related to the $R$ of the parameter ...
0
votes
1answer
69 views

Schrodinger's equation with negative sign

In time dependent Schrodinger's equation as given in Schrodinger's lecture (Four Lectures on Wave mechanics, Blackie & Son, 1949, pg22) he arrives at $$\nabla^2\psi-\frac{4 \pi m ...
8
votes
2answers
2k views

What is probability current in quantum mechanics?

What is probability current in quantum mechanics? Why define such a thing? I mean the meaning of probability current. I know the formula for it but I just don't get the idea of a flow of probability ...
2
votes
2answers
173 views

Is the sign in the Schrodinger equation physical?

I always have trouble remembering the sign in factors like $\exp(\pm ik\cdot x)$ (I'll use mostly minus signature here) that arise in field theory. My mnemonic is to remember that the Schrodinger ...
3
votes
1answer
204 views

First order coherence through double slit

The state $$|\Psi \rangle = |0\rangle + \sum_j \int d\omega f_j(\omega)\hat{a}^\dagger_j (\omega) |0\rangle $$ is coming from a far field and incident on a double slit setup. Here j is the index of ...
1
vote
1answer
282 views

Wigner Threshold law in Photodetachment and Photoionization

I am writing this question here because I have a problem in understanding the Wigner Threshold law in Photodetachment and Photoionization. The Wigner Threshold Law is given by: $\sigma$=$E^{L+1/2}$. ...
2
votes
1answer
47 views

Normalizing a wave function in a mixed well

So I got this potential and want to solve for the even wavefunctions http://imgur.com/GKAy4nD Since it's symmetric around the origin I need only to look at the interval [0,b] and solve for the ...
0
votes
3answers
54 views

Confusion about Fock subspace

I'm currently reading Folland's book on quantum field theory and came along some definitions. On p.90 of his book, Folland defines the symmetric Fock space as ...
3
votes
0answers
414 views

1D Topological insulator with PT symmetry

Assume I have the Hamiltonian for a 1D topological insulators as: $$H=\sin(P_x) \sigma_x+i \Delta \sigma_{y}+[1-m-\cos(P_x)] \sigma_z $$ where $m$ is the mass term, $P_x$ is the momentum and $\Delta$ ...
0
votes
0answers
14 views

What is the reason behind restriction imposed by no-cloning theroem on (k,n) quantum threshold scheme (QTS)?

A $(k,n)$ quantum threshold scheme (QTS) is a method to split up an unknown secret quantum state $\lvert S\rangle$ into $n$ pieces (shares) with the restriction that $k > n / 2$ (for if this ...
0
votes
3answers
96 views

Why does Hamiltonian follow the property $H^*_{ij} = H_{ji} $?

I was reading Feynman's Lectures III's Hamiltonian Matrix. There I found this property of Hamiltonian Matrix: The Hamiltonian has one property that can be deduced right away, namely, that ...
1
vote
1answer
161 views

Particle In a Box and momentum, velocity

So on a homework assignment, we are give the width of a well, $a$, and the mass of the particle $m$ and we want to find the average velocity of the particle at the n=1 state. So here is my attempt at ...
0
votes
2answers
273 views

What do “ℜe” and “A*” mean?

What do "$\mathfrak{Re}$" and "A*" mean in the following equation (taken from James Binney and David Skinner's QM lecture notes, equation 1.12), \begin{align} p(S\text{ or ...
-1
votes
0answers
59 views

How do I calculate momentum for a particle in a box, using the momentum quantum operator? [on hold]

For a particle in a one dimensional box with $U(x) = 0$ between $x = 0$ and $x = L$ (infinite Potential well) the momentum for $n = 1,2,3,...$ is given by: $$p_n = \frac{nh}{2 L}$$ The wave ...
5
votes
6answers
239 views

Why does time evolution operator have the form $U(t) = e^{-itH}$?

Let's denote by $|\psi(t)\rangle$ some wavefunction at time $t$. Then let's define the time evolution operator $U(t_1,t_2)$ through $$ U(t_2,t_1) |\psi(t_1)\rangle = |\psi(t_2)\rangle \tag{1}$$ and ...
2
votes
0answers
25 views

Perturbation theory in second quantization

I am dealing with electron/phonon interaction in QM. In particular, given the Hamiltonian of a solid, $$H=H_{el}+H_{ion}+H_{el-ion}$$ we have that the el-phonon Hamiltonian is treatened ...
0
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0answers
38 views

Simplifying a formula with Wigner d-functions

I'm following a textbook called A Group-Theoretical Approach to Quantum Optics by Andrei Klimov and Sergei Chumakov. In chapter 10, the authors calculate the Wigner function for the atomic coherent ...
0
votes
1answer
87 views

Why do $H$ and $L^2$ commute in spherically symmetric potential?

In this PDF document (a lecture by Shivaly Reddy, page 13), he says that $L^2$ is independent of $r$; therefore it commutes with any function of $r$. This seems related to a problem in ...
1
vote
1answer
39 views

Fixing time in Feynman phase space path integral

The phase space version of Feynman's path integral expression for the free particle propagator involves a (formal) sum over paths in phase space with fixed $q$ endpoints and (as far as I'm aware) ...
0
votes
0answers
52 views

Parity of $n$-photon system

The $C$-parity (charge conjugation) of an $n$-photon system is given by $(-1)^n$. If I'm not totally wrong, the intrinsic parity of a photon is $(-1)$. What is the parity $P$ of a system of $n$ ...
2
votes
1answer
171 views

Does a static electric field act continuously?

Electromagnetic radiation is emitted and absorbed in discrete units, photons. One photon's energy is described by the well known $E = hf$ formula. Now, if you a have static electric field that ...
-4
votes
0answers
56 views

Why does light travels in all directions? [on hold]

My understanding of time, gravity and speed of light: Earth revolves around the Sun. Sun revolves around Milky Way centre. Milky Way also keeps moving. All these movements are caused by gravity. ...
2
votes
1answer
104 views

What is the significance of being equivalent up to local isometry?

Background : I am reading the paper device independent outlook on quantum mechanics. The author mentions the concept of two pure states being equivalent up local isometry. From what I understood two ...
1
vote
1answer
67 views
+50

Prove that Laughlin's 3-electron states are a complete set of states

In R. B. Laughlin's 1983 Physical Review B article, Quantized motion of three two-dimensional electrons in a strong magnetic field, Laughlin separates out the center of mass motion of the electrons, ...
7
votes
1answer
201 views

spooky nonlocal communication, or bad abstract?

I'm referring to this recent paper, "Experimental Proof of Nonlocal Wavefunction Collapse for a Single Particle Using Homodyne Measurements" by Fuwa et al. published in Nature Communications. ...
0
votes
1answer
43 views

Do the eigenstates of the Pauli operators correspond to the six directions of the 3D world?

I understand that the six eigenstates of the three Pauli operators $X, Y, Z$ correspond to the six poles of the Bloch sphere. By fixing an orthonormal basis of our physical word, does "measuring Pauli ...
5
votes
2answers
865 views

How to solve bound states of 2D finite rectangular square well?

I want to solve bound states (in fact only base state is needed) of time-independent Schrodinger equation with a 2D finite rectangular square well \begin{equation}V(x,y)=\cases{0,&$ |x|\le a ...
0
votes
1answer
19 views

Number of classical oscillation modes of a Lattice and number of quantum phonons

In solving the Classical model for lattice dynamics [Rossler pag 38] we find that the lattice admits $$d\cdot N\cdot r = \#modes$$ where $d=$dimension of the problem $N=$ number of atoms $r=$ ...
1
vote
1answer
34 views

The GHZ-State in conflict with local realism

Consider three, with respect to their polarisation, entangled particles in the following state: $|\psi\rangle = \frac{1}{\sqrt2}(|H\rangle_1|H\rangle_2|H\rangle_3 + ...
2
votes
1answer
42 views

Reflection of an Electron

When a mechanical wave goes from one material to an other, some fraction of it returns back. Same thing with light (massless), but what happens with an electron? When the "wave function" changes ...
0
votes
0answers
23 views

What determines a particles probability of creation?

I know when we're discussing events at a quantum level, we deal in probability and not absolutes. What I'm looking to understand, is when articles I've read on particle physics state a particle has a ...
1
vote
2answers
171 views

Why is it easier to calculate $\langle \chi|j\rangle\langle j|A| i\rangle\langle i| \phi\rangle$ than $\langle \chi|A|\phi\rangle$?

I was reading Feynman lectures III's Spin One; there at the machinery of quantum mechanics he discusses a situation in which he needs to find the amplitude of finding the particle at ${\chi}$ state ...
2
votes
1answer
40 views

Why do the two amplitudes need to match together through the region between the boxes?

This is an excerpt from Feynman's lectures 3; Suppose we think of the situation in Fig. 7–3, which has two boxes held at the constant potentials $ϕ_1$ and $ϕ_2$ and a region in between where ...
4
votes
1answer
363 views

Why does the wave function have to be continuous? [duplicate]

When solving one dimensional problems in quantum mechanics it is often assumed that the first derivative of the wave function is continuous. What justifies this assumption?
2
votes
2answers
114 views

Probability current in scattering problems

This is a section from Wikipedia: In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection coefficients, respectively ...
29
votes
15answers
52k views

What is a good introductory book on quantum mechanics?

I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for ...
-4
votes
2answers
75 views

Quantum Entanglement - How To Interpret [duplicate]

I have thought about quantum entanglement for some time, and I still don't quite understand the reasoning behind the conclusion that entangled particles somehow can communicate their state to each ...
-1
votes
0answers
46 views

Commutation relation between linear momentum and vector Potential [on hold]

Does the linear momentum and vector potential commute? How can we show their commutation relation ? I am actually trying to find the commutation relation between both linear momentum of an electron ...
4
votes
2answers
70 views

Quantum electron and field interactions

What is the proper way to consider the electric field generated by an electron wavefunction governed by the Schrodinger equation? Can you get a result that would match observation, or is this a ...
2
votes
0answers
31 views

Conservation of momentum in Heisenberg's microscope

In working through Heisenberg's microscope, conservation of momentum for the photon and electron tells us that \begin{align} \frac{h}{\lambda}=\frac{h}{\lambda'}\sin\theta+p_x\,, \end{align} where ...
0
votes
3answers
143 views

Why is only one quantity of angular momentum i.e. $L_z$ quantized & not $L_x$ & $L_y$?

This is quoted from Arthur Beiser's Concepts of Modern Physics: Why is only one quantity of $\mathbf{L}$ quantized? The answer is related to the fact that $\mathbf{L}$ can never point in any ...
3
votes
1answer
25 views

One Pion Exchange Potential properties for a two-nucleon system

I'm going through my Nuclear Physics book, and has come across a section called "Properties of OPEP for the two-nucleon system". It start out by considering the n-p system in a singlet spin state ...
4
votes
1answer
240 views

Does tunneling transmission probability depend on the density of states or velocity?

In some quantum text books [1], the tunneling transmission formula depends only on the density of states of 2 regions (DOS) involved in tunneling. ($T(E) = C \times DOS_1(E) \times DOS_2(E)$, where C ...