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 ...

learn more… | top users | synonyms (4)

10
votes
2answers
1k views

Schrodinger equation in spherical coordinates

I read a paper on solving Schrodinger equation with central potential, and I wonder how the author get the equation(2) below. Full text. In Griffiths's book, it reads ...
7
votes
2answers
4k views

Solving one dimensional Schrodinger equation with finite difference method

Consider the one-dimensional Schrodinger equation $$-\frac{1}{2}D^2 \psi(x)+V(x)\psi(x)=E\psi(x)$$ where $D^2=\dfrac{d^2}{dx^2},V(x)=-\dfrac{1}{|x|}$. I want to calculate the ground state ...
2
votes
3answers
283 views

Hydrogen transition and photon behavior

consider a transition for an electron in the Hydrogen atom from the ground state to the 1st excited state. Let's say this transition occurs through absorption of a photon of exactly the energy ...
3
votes
1answer
345 views

SO(3) x SU(2) Symmetry of the Hamiltonian

I have a question converning multiplets when describing atoms. Let $H=\sum\limits_{k=1}^{N} (p_{k}^2 - \frac{Z}{|x_{k}|} + \sum\limits_{i<k}^{1..N} \frac{1}{|x_{i} - x_{k}|}$ be a (self-adjoint) ...
-1
votes
1answer
458 views

Heisenberg's Uncertainty Forms

Can Heisenberg's Uncertainty principle be rewritten in terms of energy density writing $$\Delta E \Delta T \geqslant \hbar/2$$ in factors of energy density $\Delta \sigma \text{ }= \frac{3\Delta ...
4
votes
2answers
391 views

Mixed state after measurement

I'm looking at Section 2.4.1 of Nielsen and Chuang's Quantum Computation and Quantum Information were they derive the density operator versions of the evolution and measurement postulates of quantum ...
4
votes
2answers
1k views

On numerically solving the Schrödinger equation

I just read a paper 'A pocket calculator determination of energy eigenvalues' by J Killingbeck (1979). Link: http://iopscience.iop.org/0305-4470/10/6/001 I have some questions about section 2. Why ...
18
votes
6answers
1k views

Why can we treat quantum scattering problems as time-independent?

From what I remember in my undergraduate quantum mechanics class, we treated scattering of non-relativistic particles from a static potential like this: Solve the time-independent Schrodinger ...
3
votes
2answers
3k views

Quantum momentum (De Broglie)

The de broglie hypothesis suggests a particle can be associated with a wave of momentum $p = \hbar k$ my question is the following: how does one arrive at this concept of the momentum of a wave? I ...
4
votes
3answers
69 views

Can the Hanbury-Brown and Twiss effect be used to measure the size of composite objects like galaxies?

I know that the Hanbury-Brown and Twiss effect can be used to measure the size of stars. Can it also be used to measure the size of galaxies?
11
votes
2answers
572 views

Essential background for QFT study

The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations: $$\frac{d\sigma}{d\Omega} = ...
3
votes
1answer
210 views

Does decoherence single out a preferred frame?

Environmentally induced decoherence makes wave function collapse unnecessary. But the environment, usually taken to be some heat bath, introduces a preferred frame. (That in which the total (spatial) ...
5
votes
2answers
311 views

Two paths having the same phase in the path integral approach

In the path integral approach to Quantum Mechanics, can two distinctly different paths of the possible infinite paths have the same phase, i.e can there be a bimodal distribution of the phases ...
2
votes
2answers
575 views

Operator relation involving the logarithm of an operator?

Dirac gives the relation: $\exp(iaq)f(q,p) = f(q, p - a\hbar)\exp(iaq)$ where $\hbar$ is Planck's constant. Can anybody give me the corresponding relation when the $\exp$ function is a $\ln$?
1
vote
4answers
228 views

Quantum dots on the nuclear scale!

Quantum dots are quantum systems that are confined by definition on the nano scale. Why didn't people study similar systems on a much smaller scale, something as small as the dimension of the nucleus? ...
2
votes
1answer
586 views

Atomic Transitions - Dipole Approximation

my question concerns the interaction of light and matter in a semi-classical approach. (Quantized Atoms, Classical Fields) In the Coulomb gauge (div A = 0 , $\phi$=0) we have $E = ...
9
votes
2answers
1k views

Poincare group vs Galilean group

One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
3
votes
1answer
268 views

Coincidence detectors in Bell tests: How close is close enough?

When is a coincidence a coincidence? We know that to identify entangled photons, the electronics is set to look for simultaneous clicks at opposite detectors. The size of the window is to some degree ...
4
votes
1answer
423 views

Commutation of operators in quantum theory

I have always written the commutation rules of quantum theory as , $[q,p] = i\hbar\delta _{ij}$ But seems that some people write this as, $[q^i,v_j]= \frac{i\hbar}{M}\delta^i _{j}$ (..this is ...
3
votes
3answers
799 views

Time in special relativity and quantum mechanics

The time is treated differently in special relativity and quantum mechanics. What is the exact difference and why relativistic quantum mechanics (Dirac equation etc.) works?
11
votes
7answers
1k views

Quantum entanglement vs classical analogy

Consider that we have two balls, one white and one black, and two distant observers A and B with closed eyes. We give the first ball to the observer A and the second ball to the observer B. The ...
2
votes
1answer
638 views

About the delta potential well

If a particle in a delta potential well has negative energy, why the particle will be bound in the well? And if it has positive well, why it is free to move in either half-space: x < 0 or x > 0? I ...
2
votes
5answers
905 views

Radio waves within an atom

What effect does the quantum world have on radio waves? For example, if I could shrink myself down and stand on the nucleus (or even smaller sub atomic particles making up the nucleus) with a device ...
12
votes
1answer
3k views

Solving Schrödinger's equation with Crank-Nicolson method

I am trying to numerically solve Schrödinger's equation with Cayley's expansion ($\hbar=1$) $$\psi(x,t+\Delta t)=e^{-i H\Delta t}\psi(x,t)\approx\frac{1-\frac{1}{2}i H\Delta t}{1+\frac{1}{2}i H\Delta ...
3
votes
1answer
1k views

What is the Jost function in scattering theory?

What is the Jost function in scattering theory? Is it an operator or some kind of determinant? How is it obtained?
3
votes
1answer
346 views

Stern-Gerlach-Experiment with j=1 atoms?

Suppose you do a Stern-Gerlach experiment with atoms in a $j=1$ state. There would be three separate beams ($m_j = -1, 0, 1$) coming out of the apperatus. But what would be the relative distribution ...
5
votes
3answers
613 views

Defining Measurement in Quantum Mechanics

I should begin by saying that I am a total newbie when it comes to Quantum Mechanics. Therefore my question might sound metaphysical to people who know their stuff. So please forgive. What I am ...
8
votes
2answers
287 views

Observables with transcendental eigenvalues

Are there any "natural" physical observables which have non-empty point spectrum which consists of numbers which are not algebraic numbers?
3
votes
2answers
1k views

What potential energy functions are mostly used in Schrodinger equation?

In the time-independent Schrodinger equation $$\left(-\frac{\hbar^2}{2m}\Delta+V(\mathbf{r})\right)\psi(\mathbf{r})=E\psi(\mathbf{r})$$ What functions $V(\mathbf{r})$ are mostly used in research ...
6
votes
3answers
1k views

Are there any practical applications of the uncertainty principle

I believe GPS works because of extremely small time differences between the satellites. Because of how small the time differences are, it needs to take into account gravity's effect on time. ...
29
votes
4answers
3k views

What really cause light/photons to appear slower in media?

I know that if we solve the Maxwell equation, we will end up with the phase velocity of light being related to the permeability and the permittivity of the material. But this is not what I'm ...
3
votes
1answer
204 views

Why is the local field algebra $\mathfrak F(O)$ associated with a bounded non-empty open region $O$ of space-time not irreducible?

Let us consider a Wightman field theory for the free scalar neutral field $\phi$, and let $O\mapsto\mathfrak F(O)$ be the net of local von Neumann field algebras. If we take a non-empty bounded open ...
-1
votes
1answer
277 views

What the theta in schwinger function and what is theta formula?

What the theta in schwinger function and what is theta formula? is theta formula general solution of klein gordon equation? if so, what is its coefficient of $\exp\left(-ipx\right)$?
8
votes
2answers
233 views

Finding the spectrum of a polynomial of the creation and annihilation operators

Is there a general algorithm to find the spectrum of $S S^\dagger$, where $S$ is a homogenous polynomial (of degree $n$) of the annihilation operators (of $d$ variables)?
4
votes
1answer
627 views

Wave function normalization

A book by C. J. Ballhausen led me to believe that a quick way to check that I performed step operators properly was by observing that the "wave function should appear normalized," but I have found ...
4
votes
2answers
489 views

What happens where an electron is annihilated by a spontaneously generated positron-electron pair?

I was visiting the Australian Synchrotron earlier today as part of a tour group; as the guide was going over the booster and storage rings I was reminded of something I learnt of quantum. If I know ...
14
votes
5answers
1k views

What is Hawking radiation and how does it cause a black hole to evaporate?

My understanding is that Hawking radiation isn't really radiated from a black hole, but rather occurs when a particle anti-particle pair spontaneously pop into existence, and before they can ...
4
votes
3answers
457 views

How could a particle be isolated to avoid decoherence?

The question aims to this issue : if there is some technological arrangement (or action) to take over the particle/system in order to keep it in a coherent state, then the field, (force or whatever) ...
4
votes
2answers
282 views

Clebsch-Gordan Identity

I'm trying to take advantage of a particular identity for the sum of the product of three Clebsch-Gordan coefficients, however, the present form of my equation is slightly different. Is there a ...
2
votes
3answers
373 views

Fermionic interaction potentials

Are there any examples of fermionic particles or quasiparticles for which the interaction potential is a globally smooth function? i.e. no singularities or branch points. As an example, in Flügge's ...
2
votes
1answer
203 views

Church–Turing Thesis

Can the Church–Turing Thesis be proved assuming classical mechanics, how is the proof or disproof? Edited: I was looking for a proof of "everything computable by a device obeying CM is computable by ...
11
votes
3answers
991 views

When is the “minus sign problem” in quantum simulations an obstacle?

The "minus sign problem" in quantum simulation refers to the fact that the probability amplitudes are not positive-definite, and it is my understanding that this leads to numerical instability when ...
4
votes
2answers
234 views

Phase of Elements

There are 11 gaseous elements and two liquid elements at standard temperature and pressure. The rest are solid. Can phase be predicted from quantum mechanical principles?
5
votes
4answers
1k views

Is Quantum Physics used in manufacturing CPUs?

If I remember correctly, I heard some people saying that the transistors on CPUs today are so small, that they have to use quantum physics to make CPUs. Is that correct?
3
votes
1answer
154 views

generalizing spin rotations

I have a question about the relation: $\exp(-i \vec{\sigma} \cdot \hat{n}\phi/2) = \cos(\phi/2) - i \vec{\sigma} \cdot \hat{n} \sin(\phi/2)$. In my texts, I see $\phi\hat{n}$ always as c-numbers. My ...
6
votes
1answer
882 views

What is the meaning of the Fourier transform of Feynman propagator?

I know $K(a,b,t)$ is the probability amplitude that a particle that starts at point $a$ is found at point $b$ at a time $t$ later. There is also an expression that sometimes is called green function: ...
4
votes
3answers
483 views

Very simple example of the way the Fourier transform is used in quantum mechanics?

According to a book I'm reading, the Fourier transform is widely used in quantum mechanics (QM). That came as a huge surprise to me. (Unfortunately, the book doesn't go on to give any simple examples ...
4
votes
1answer
773 views

Does this new quantum experiment rule out the possibility of a many-worlds interpretation?

This brand new published result (nature): Experimental non-classicality of an indivisible quantum system by Radek Lapkiewicz, Peizhe Li, Christoph Schaeff, Nathan K. Langford, Sven ...
3
votes
2answers
587 views

The most price-efficient experimental setup involving SPDC, single-photon counting etc

I would like a suggestion on a price-efficient way of experimenting with spontaneous down-conversion and single-photon counting. The simple dual-slit experiment could be one part of an application ...
1
vote
0answers
226 views

Macroscopic superposition of humans and past thoughts? [closed]

Decoherence apparently only works if a lot of degrees in the environment are measured with infinitely many copies reaching to all eternity. If too few memories and records survive with infinitely many ...