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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143 views

Kinetic energy (KE) in atomic orbital

Within an atomic orbital, electrons must obviously have relative differences between points in space due to potential gradient. But there is kinetic energy as well. If we choose a particular point as ...
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1answer
26 views

Plane wave expansion of cylindrical functions:Summation of the Hankel functions

I understand that; in cylindrical coordinates, the basic solutions of the Helmholtz equation are of the form Hankel function of integer order times a complex exponential term ...
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1answer
52 views

Fillings of dispersion bands (E-K diagram)

I struggle in understanding why in some references the bands filling by electrons in the E-k diagram is shown as an area delimited below by the dispersion curve and above by the Fermi energy (if in ...
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18 views

relations opf space-time to gravitation as an evolutionary process [on hold]

just thoughts - 1 -gravity - could it be that it is not a fundamental force after all - could it be that it evolved after the big bang? space time was evolving and things [lets call them string but ...
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1answer
147 views

A few questions on wave packets and uncertainty relations

According to Cohen-Tannoudji the wave-function for a one-dimensional free particle can be written as $$ \psi (x,0)=\frac{1}{\sqrt{2 \pi}} \int g(k) e^{ikx} dk.$$ While $g(k)$ is not specified, there ...
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95 views

Algebraic solution of Dirac equation for Coulomb potential

The Runge-Lenz operator enables an algebraic solution of Coulomb potential energy levels without a solution of a differential equation. What is the analog for the solution of the Dirac equation in a ...
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2answers
325 views

Hydrogen atom: potential well and orbit radii

I happened to open up an old solid-state electronics book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level En" The orbit radius is ...
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2answers
1k views

Coupled quantum harmonic oscillator

Given the following Hamiltonian for two identical linear oscillators with spring constant $k$ and interaction potential $\alpha x_1x_2$; I was asked to find the expectation value $\langle ...
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1answer
61 views

Does the Heisenberg uncertainty principle preclude moving in a straight path with certainty?

The uncertainty principle is σₓσₚ ≥ 0.5 ℏ where x is position and p is momentum. Consider a 2d plane. If one moves along a straight line along the plane (possibly backtracking or moving forwards but ...
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723 views

The uncertainty principle and black holes

What are the consequences of applying the uncertainty principle to black holes? Does the uncertainty principle need to be modified in the context of a black hole and if so what are the implications ...
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0answers
69 views

Spin 1/2 particle in rotating magnetic field [on hold]

So, I'm attempting a solution to the following problem: I am given a particle with spin 1/2 in a constant vertical magnetic field and a rotating field in the (x,y) plane. $$B(t) = [B_1\cos(\omega ...
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1answer
110 views

Probability conservation in WKB tunneling

Suppose we have quantum mechanical plane waves of energy $E$ incident upon a one-dimensional potential barrier $V(x)$ with sloping sides. One can compare the WKB solutions in the three relevant ...
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1answer
176 views

Correct way to do a Thomas-Fermi approximation for cold gases

I have calculated the total Gross-Pitaevskii energy for a 2D Bose-Einstein condensate in an harmonical trap, using a variational gaussian wave function with a variational parameter b. Now I want to ...
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1answer
50 views

How is light slowing down in a medium thought of in the photon picture? [duplicate]

The speed of light in any medium besides vacuum is smaller than $c$. In a classical way, I just look at that as a wave that propagates less fast, the change in EM-field is passed on slower. How should ...
2
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2answers
47 views

Why does transmission probability decrease, increase, then decrease again?

We did a quantum tunneling lab online. We used a Java program to model the electron wave function and show what happens when there is a step potential (U is less than E). Our value for the ...
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0answers
42 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 $n$ ...
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3answers
197 views

Constructing solutions to the time-dependent Schrödinger's equation

The following question is from David Griffiths' Introduction to Quantum Mechanics: Problem 2.13 A particle in the harmonic oscillator potential starts out in the state $$\Psi(x,0) = A[3 ...
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1answer
65 views

Is the Energy of an absorbed photon exactly the energy of the band gap?

I was wondering, if the Energy of a Photon which is absorbed by an Electron, hast to be exactly the Energy of the bound gap. So if i have two energy levels in an atom $E_2$ and $E_1$, does my ...
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5answers
107 views

Does measurement change the evolution of wave function?

Basically any measurement is on wave function $|\psi\rangle$ is done by operator $X$ such that $X|\psi\rangle$ results observable $x$ with some probability. But what happens to $|\psi\rangle$? Does ...
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3answers
99 views

Must the product of the two complementary quantities in an uncertainty relation have unit $\text{Js}$?

I know that the uncertainty principle is: $$\Delta p\Delta q \ge \frac{\hbar}{2}.$$. But do the units on the left-hand side of the equation always have to equal $\text{Js}$, i.e. $\text{energy} ...
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0answers
13 views

Spherical representation of field operators of scalar field [on hold]

I want to ask how to construct the field operators using spherical harmonics.... of a scalar field operator ?
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2answers
127 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
3
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3answers
155 views

How to connect these two formulations regarding the need for a density matrix in quantum mechanics?

I found these two formulations: The density matrix is: 1) "needed if we consider a system that is part of a larger closed system." 2) "needed for a system to be ...
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1answer
119 views

What really generates time evolution?

A fundamental principle of quantum mechanics, as far as I can tell, states that the Hamiltonian generates time evolution. A common result about generators are the following: let $\mathrm T$ be the ...
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2k views

Why are scattering matrices unitary?

In Griffith's QM book, he introduces scattering matrices as an end-of-the-chapter problem. For a Dirac-Delta potential $V(x) = \alpha \delta (x - x_0)$, I've derived the scattering matrix and ...
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0answers
27 views

Fourier transformation and mode expansions [duplicate]

Sorry as this is a rather trivial question, but I'm stuck with a certain implication. I'm working on exercise 1.7 from Polchinski where we are given an open string with boundary conditions ...
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1answer
38 views

Time dependence of the displacement operator

I am following the derivation of the master equation (and application of this) in these lecture notes. Unfortunately I do not follow the step of eliminating the driving terms of the harmonic ...
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2answers
85 views

How does a photon leave trace of its polarization state in a photon detector but not trace of which direction it came in?

Some quantum erasure experiments involve polarization of photons. In one such experiment with a double slit, a horizontal polarizer is used in front of one slit, and a vertical polarizer is used for ...
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2answers
228 views

Oscillation of a Bose Einstein condensate in a harmonical trap

We were asked to try to make a theoretical description of the following phenomenon: Imagine a 2D Bose Einstein condensate in equilibrium in an harmonical trap with frequency $\omega$. Suddenly the ...
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1answer
123 views

What is many-body bound state?

Bound state by definition is a state when particles are bounded together, so then "many-body bound state" would be bound state for a system of many bodies. Then I have several puzzles: 1. is the state ...
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0answers
85 views

Fourier transformation and commutators

Sorry as this is a rather trivial question, but I'm stuck with a certain implication. I'm working on exercise 1.7 from Polchinski where we are given an open string with boundary conditions ...
1
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0answers
74 views

Particle annihilation - mathematical description, equations governing it? [duplicate]

I was wondering about this and I would like to know an explanation why do particles and antiparticles annihilate? I would be interested in phenomenological, but most importantly mathematic explanation ...
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4answers
3k views

Is quantum entanglement functionally equivalent to a measurement?

I saw the following talk the other day: http://www.youtube.com/watch?v=dEaecUuEqfc&feature=share In it, Dr. Ron Garret posits that entanglement isn't really that "special" of a property. He ...
4
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1answer
244 views

Time-dependent Schrodinger equation from variational principle

In the paper, "Density-functional theory for time-dependent systems" Physical Review Letters 52 (12): 997 the authors mentioned that the action $$ A= \int_{t_0}^{t_1} dt \langle \Phi(t) | i ...
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2answers
94 views

Integration by parts to derive $d\langle x \rangle / dt$

I am reading "Introduction to Quantum Mechanics" by David Griffiths and I am having trouble understanding part of a derivation of $\frac{d\langle x\rangle }{dt}$ in section 1.5 - Momentum - of the ...
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3answers
574 views

Why does nonlinearity in quantum mechanics lead to superluminal signaling?

I recently came across two nice papers on the foundations of quantum mechancis, Aaronson 2004 and Hardy 2001. Aaronson makes the statement, which was new to me, that nonlinearity in QM leads to ...
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1answer
56 views

Solution of the Radial Part of the Schroedinger Equation [closed]

The general Schroedinger Equation is: $$\left[-\frac{\hbar^2}{2m}\triangle +V(r,\vartheta,\varphi)\right]\psi_{nlm}=E\psi_{nlm}$$ When considering free waves, i.e. $V(r,\vartheta,\varphi)=0$ and a ...
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0answers
18 views

Fun physics book for high school student [duplicate]

can anyone recommend me a physics book for a highschool student (not these typical school books) a book that will let you think mostly interested in theoretical /quantum physics done with the ...
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0answers
33 views

Why Electron Does Not Radiate In Bohr Orbits? [duplicate]

Maxwell said that charged particles radiate when are in accelarating motion. I understand that $nλ=2πr$ must be fulfilled in order to create a sinusoidal standing wave and to satisfy the probability ...
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1answer
52 views

Quantum computing can be done via measurement alone, why is this significant?

I read in the Afterword section of Nielsen and Chuang's book Quantum Computation and Quantum Information that A second area of progress has been in understanding of what physical resources are ...
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1answer
95 views

How to visualize a Schrödinger cat state?

I recently read about Schrödinger cat states (SCS), which are basically a superposition of two coherent states $|\alpha\rangle$ with opposite phases, that is, $$ |cat\rangle = |\alpha\rangle \pm ...
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1answer
33 views

Preventing Heat Escape

Is is possible to completely prevent heat from escaping from a closed container? Here is a diagram of vacuum flask, which tries to implement the design - Vacuum Flask prevents heat from escaping ...
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4answers
103 views

Can a photon have little to no energy and/or speed?

Can a photon move more slowly than the speed of light and behave 'non-relativistically,' so to speak. Perhaps another way to express my thought is: could we stop a photon from moving?
3
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1answer
339 views

Hubbard Model Hamitonian

$H = -\sum\limits_{i,j} A_{ij} c_i^{\dagger} c_j + \frac{U}{2} \sum\limits_i(c_i^\dagger c_i)(c_i^\dagger c_i -1)$ is defined to be a Hamiltonian for modeling quantum random walk of identical ...
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1answer
258 views

Why is the orbital angular momentum of a pi electron along the axis of two atoms' molecule one?

I'm reading quantum chemistry. The book says that the orbital angular momentum of a $\pi$ electron along the symmetry axis of a molecule made up of two atoms is $\pm 1$. I think this is a primary ...
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0answers
55 views

Probability flux

I was reading a text on Quantum Mechanics in which it said that $$\int{d^3 x \, j(x,t)} = \frac{\langle p\rangle}{m},$$ where $\langle p\rangle$ is the expectation value of the momentum operator at ...
3
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1answer
127 views

Approximating a target operator

I was wondering if anyone knew how the author got to equation 12 on page four of this paper, I will attempt to explain the situation below. Given $C$, a target operator, we wish to create an ...
3
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2answers
158 views

Quantum mechanics and the atom

I was thinking about the nature of the atom, specifically, why electrons do not spiral into the nucleus. My physics book says the principal quantum number $n$ must be an integer number of wave ...
47
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4answers
7k views

What is spin as it relates to subatomic particles?

I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does ...
2
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1answer
88 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 ...