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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448 views

When you apply the spin operator, what exactly is does it tell you?

The example I'm trying to understand is: $ \hat{S}_{x} \begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}} \end{pmatrix} = 1/2 \begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}} ...
6
votes
1answer
254 views

Equivalent Representations of Clifford Algebra

I'm reviewing David Tong's excellent QFT lecture notes here and am a little confused by something he writes on page 94. We've considered the standard chiral representation of the Clifford Algebra, ...
2
votes
2answers
169 views

In a double slit experiment are any particles lost because they hit the space between the two slits?

In its wave-form a particle should pass through every time because it propagates in all directions. So there shouldn't be any losses of particles landing in between the slits, right?
8
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2answers
599 views

Was uncertainty principle inferred by Fourier analysis?

I would like to know: did Heisenberg chance upon his Uncertainty Principle by performing Fourier analysis of wavepackets, after assuming that electrons can be treated as wavepackets?
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0answers
99 views

Does quantum Zeno effect play role in astrophysics?

For example, do two galaxies situated in proximity reduce the atom decay rate in each other? What happens with decay quanta escaped to infinity? Does the radius of apparent horizon effect the ...
3
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4answers
693 views

Why, for a spin-½ particle, are the possible outcomes of measuring spin projection along any direction the same?

If one measures the projection of spin of a spin half particle along the $x$ axis one will always get $\pm\tfrac12\hbar$. Measuring it along the $y$ axis one will always get $\pm\tfrac12\hbar$. ...
3
votes
2answers
224 views

Reference request for the Aharonov-Bohm effect

I am looking for a good reference to an online source or book, on the magnetic Aharonov-Bohm effect. I have read the appropriate sections from the book by Griffiths and Ballentine, and still haven't ...
2
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1answer
1k views

A Short way to show Conservation of Quantum Laplace–Runge–Lenz Vector?

I had been asked to prove the conservation of Quantum Laplace–Runge–Lenz Vector: ...
12
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3answers
3k views

Simple explanation of Quantum Zeno Effect

I'm a student and I had to give a talk on seminar about Quantum Zeno effect and Anti-Zeno effect to my colleagues (all listeners have had a course in quantum physics, but not a heavy one with all the ...
11
votes
1answer
542 views

What are the 't Hooft papers about classical models underlying QM?

Gerard 't Hooft states on his webpage: I have mathematically sound equations that show how classical models generate quantum mechanics. Also, there are some interesting discussions here on ...
4
votes
3answers
714 views

What is the experiment where subatomic particles appear to foresee the future?

I've seen a documentary, whose name I don't remember but I'm curious because it suggests that subatomic particles are able to "foresee the future". I'll try to describe it here: Some particles are ...
7
votes
1answer
695 views

Classical vs. Quantum use of the spin 4-vector

I have a few basic questions about the Pauli-Lubanski spin 4-vector S. I've used it in quantum mechanical calculations as an operator, that is to say each of the components of S is a matrix operator ...
8
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1answer
662 views

exponential potential $ \exp(|x|) $

For $a$ being positive what are the quantisation conditions for an exponential potential? $$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$ with boundary conditions $$ y(0)=0=y(\infty) $$ I ...
3
votes
2answers
351 views

Definition of “Quantizing”

Could anyone explain to me what "quantize" means in the following context? Quantize the 1-D harmonic oscillator for which $$H~=~{p^2\over 2m}+{1\over 2} m\omega^2 x^2.$$ I understand that the ...
2
votes
1answer
168 views

Can you tell if a particle is in superposition?

This may be an easy answer for anybody. Is it possible to detect if a particle A is still in a superposition via the sending a group of particles B through a box containing particle A?
4
votes
1answer
231 views

Wigner's friend and quantum Zeno effect

Suppose Winger's friend is placed into a black box, thoroughly isolated from the outside world. He constantly observes an atom with a delay of some microseconds. According to Zeno effect, atom's ...
21
votes
4answers
5k views

Amplitude of an electromagnetic wave containing a single photon

Given a light pulse in vacuum containing a single photon with an energy $E=h\nu$, what is the peak value of the electric / magnetic field?
1
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0answers
82 views

Calculating the error by a small change of the potential in Schrodinger equation

In $\mathbb{R}^3$, consider the time-dependent (non-rel) Schrodinger equation with the potential energy $V(\mathbb{x})$. When a small change(e.g., just a small constant $\delta>0$) of V(x) is ...
1
vote
1answer
121 views

Noise spectrum of two systems and interacting Hamiltonian

I've been discovering recently the concept of noise spectrum, defined as: $$S_{xx}[\omega] = \int dt \langle x(t)x(0)\rangle \text{e}^{-i\omega t}$$ Roughly the Fourrier transform of the two-point ...
2
votes
3answers
2k views

Fermi's Golden Rule and Density of States

I know Fermi's Golden Rule in the form $$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2$$ where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition ...
3
votes
2answers
251 views

Interpretation of $e|\psi|^2$ as electron density

In solid state physics the electron density is often equated to $e|\psi|^2$. However, the Sakurai says (Chapter 2.4, Interpretation of the Wave Function, p. 101) that adopting such a view leads "to ...
2
votes
2answers
2k views

What's the physical significance of the inner product of two wave functions in quantum region?

I am a reading a book for beginners of the quantum mechanics. In one section, the author shows the inner product of two wave functions $\langle\alpha\vert\beta\rangle$. I am wondering what's the ...
8
votes
3answers
247 views

Is $k_B \rightarrow 0$ the classical limit of stat. mech., as $\hbar \rightarrow 0$ is in QM?

I hear very often among my peers and seniors that just as how $\hbar\rightarrow0$ takes me to classical mechanics from quantum mechanics, $k_B\rightarrow0$ will take me to classical thermodynamics ...
3
votes
0answers
433 views

Hamiltonian of the surface states of a 3D topological insulator

The surface states of a 3D topological insulator (let's say in the (x-y) plane) are sometimes described by the following Hamiltonian : $$H(k)=\hbar v_F (p_x \sigma_x + p_y \sigma_y)$$ or sometimes by ...
8
votes
1answer
536 views

Operator Ordering Ambiguities

I have been told that $$[\hat x^2,\hat p^2]=2i\hbar (\hat x\hat p+\hat p\hat x)$$ illustrates operator ordering ambiguity. What does that mean? I tried googling but to no avail.
12
votes
3answers
4k views

Schrodinger's equation (explanation to non physicist)

For a report I'm writing on Quantum Computing, I'm interested in understanding a little about this famous equation. I'm an undergraduate student of math, so I can bear some formalism in the ...
5
votes
1answer
161 views

Constructing the space of quantum states

I want to learn how to construct spaces of quantum states of systems. As an exercize, I tried to build the space of states and to find hamiltonian spectrum of the quantum system whose Hamiltonian is ...
3
votes
2answers
700 views

Zero point fluctuation of an harmonic oscillator

In a paper, I ran into the following definition of the zero point fluctuation of our favorite toy, the harmonic oscillator: $$x_{ZPF} = \sqrt{\frac{\hbar}{2m\Omega}} $$ where m is its mass and ...
1
vote
1answer
1k views

Adjoint of momentum operator

In position basis, we have, $$\langle x \mid \hat p \mid \Psi(t) \rangle = -\imath \hbar \frac{\partial{\langle x \mid \Psi(t) \rangle}}{\partial{x}} $$ Now I know $\hat{p}$ is a Hermitian operator ...
5
votes
1answer
265 views

Expectation value calculation for a weird operator

In the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups.- E weinberg I am not being able to see one of the calculation. The author states (eqn 3.26) $$\langle ...
1
vote
1answer
467 views

Does a particle in a spherically symmetric infinite square well potential exert a force on the inner and outer shell barrier?

For a particle in the potential: $$V(r) = \begin{cases} 0 & \text{a < r < b}\\ \infty & \text{otherwise.} \end{cases}$$ Does this guy in the ground-state exert a force on the shells a ...
2
votes
0answers
248 views

How to calculate radiative transition rate of exciton in a quantum dot with specific dimension?

I am writing rate equations for a nanophotonic system including three quantum dots. I need to calculate that radiative transition rates of exciton in ground state in those quantum dots. In the paper ...
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vote
2answers
584 views

Angular Momentum Operators Non-Degenerate

Typically one writes simultaneous eigenstates of the angular momentum operators $J_3$ and $J^2$ as $|j,m\rangle$, where $$J^2|j,m\rangle = \hbar^2 j(j+1)|j,m\rangle$$ $$J_3 |j,m\rangle = \hbar ...
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votes
2answers
675 views

A thought experiment with Heisenberg's Uncertainty Principle [duplicate]

Possible Duplicate: Could the Heisenberg Uncertainty Principle turn out to be false? Thought Experiment Ponder, for a moment, if I had a cube with 10cm sides which I'll name The Box. By ...
7
votes
4answers
9k views

How do electrons jump orbitals?

My question isn't how they receive the energy to jump, but why. When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals ...
5
votes
2answers
451 views

WKB method of approximation

Would it be legitimate to use the WKB approximation for a particle in a spherically symmetric Gaussian potential? $$V(r)~=~V_0(1-e^{-r^2/a^2}).$$ I'm not sure when to use which approximation ...
0
votes
2answers
97 views

Quantum Conservation versus classical conservation

If energy is conserved in all quantum mechanical interactions, how are there classical interactions in which energy is not conserved, given that classical interactions are a macroscopic approximation ...
1
vote
2answers
583 views

Double slit experiment alternating holes

If we perform the double slit experiment by shoting photons covering one hole at a time, would we see equally the double slit interference?. That is, the same set up of double slit but fire photons ...
2
votes
1answer
140 views

Potential of particle exchange

There are two heavy particles (of mass $M$) and a light one (of mass $m<<M$). The light particles interact with heavy particle with an attracting dirac delta potential ...
0
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2answers
225 views

Differential of Quantum mean value or expectation value

How to take differential of Quantum mean value over hermitian operator (mean or expectation value)? $$d\langle \hat A\rangle$$ remark: or time evolution of mean value over operator $$\frac {d\langle ...
6
votes
1answer
333 views

few fermions in a harmonic trap — position density matrix from diagrammatics

I'm trying to calculate the momentum distribution of a 1D system of non-interacting identical fermions in a harmonic trap. Given Feynman's answer (from his Statistical Mechanics book) for the ...
0
votes
0answers
72 views

Why is the transition into N proportional to N+1?

I am having trouble understanding the origin of the bosonic stimulated emission. How can I qualitatively understand why bosons Boson's attract each other into similar quantum states. The furtherst I ...
2
votes
2answers
772 views

Non-Degeneracy of Eigenvalues of Number Operator for Simple Harmonic Oscillator [duplicate]

Possible Duplicate: Proof that the One-Dimensional Simple Harmonic Oscillator is Non-Degenerate? I'm trying to convince myself that the eigenvalues $n$ of the number operator ...
1
vote
1answer
164 views

Commutation relation of $J^2$ and $R(\alpha,\beta,\gamma)$

If $R(\alpha,\beta,\gamma)$ is the Rotation operator and $\alpha,\beta,\gamma$ are Euler angles and $J$ is the total angular momentum then how to get to this: $$[J^2,R]~=~0?$$ This is stated in ...
8
votes
3answers
1k views

Force through quantum mechanics

In classical physics force is: $$F=\frac {dp}{dt}$$ How about quantum mechanics? In Old Quantum Mechanics momentum is: $p=\hbar \cdot k$ so force will be: $$F=\hbar \frac {dk}{dt}$$ what does $\frac ...
2
votes
2answers
4k views

Two expressions for expectation value of energy

I was looking up expectation value of energy for a free particle on the following webpage: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html It says that $E=\frac{p^2}{2m}$ and ...
0
votes
2answers
1k views

Showing that the probability density of a linear harmonic oscillator is periodic

The complete question I am trying to answer is the following: Show that the probability density of a linear harmonic oscillator in an arbitrary superposition state is periodic with period equal to ...
3
votes
1answer
267 views

Decay of a particle

Would someone please explain the following found on P. 125 of these notes? On the other hand, two $π^0$’s cannot be in an $l = 1$ state. The reason for this is that pions are bosons and so the ...
2
votes
1answer
647 views

What is the spatial mode of light or the spatial mode of a massive particle?

I'm extremely confused by what physicists mean by the spatial mode of light. I am also equally if not more confused by what the spatial mode of a massive particle is. Can anyone help me out by ...
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0answers
189 views

What is the link between the density matrix and Hestenes' spinors in geometric algebra?

The density matrix (or state matrix) is a generalization of a wave function that is able to describe incoherent superpositions of an N-state system. It is often written as a matrix and observables are ...