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)

1
vote
1answer
750 views

Force exerted on potential wall

A particle bound in an infinite potential wall at $x=0$ will apply a force on the wall. For a plane wave and imagining it as a fluid bouncing off the reflection wall at $x=0$, find the force in terms ...
1
vote
1answer
306 views

Symmetry and overlapping of ground states

In a quantum mechanics, there is the following formula to derive the zero energy $E_0$ of a perturbed Hamiltonian $$H = H_0 + V$$ knowing the zero energy $W_0$ of the free Hamiltonian $H_0$: $$E_0 = ...
10
votes
6answers
2k views

What constitutes an observation/measurement in QM?

Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle. What is the technical definition of an observation/measurement? If I look at a QM system, it ...
1
vote
1answer
109 views

How to solve the tranmission probability in an evolution of a quantum system

I've just learned the evolution of some quantum system for about a week, and our homework sometimes something like this. I don't quite have any idea of solving this kind of problem. Can you help ...
2
votes
1answer
152 views

Does wavefunction reach its largest peak near(not in) the classical forbidden region?

As we can see in the picture in this website: http://ctz116.ust.hk/xyli2/images/animation/quchem73.html It's strange that the bound state wavefunction always reach its largest peak near the boundary ...
0
votes
1answer
141 views

A Derivation of Ehrenfest's Theorem in a particular case

What are the missing lines in the integration? $$\frac{\text d \langle {p} \rangle}{ \text{d} t} $$ $$= \frac{\text d}{\text d t} \int\limits_{-\infty}^{\infty} \Psi^* \left( ...
3
votes
1answer
663 views

Feynman diagrams and Hartree-Fock

I am puzzled by some lines I read in Mattuck's book on Feynman diagrams in many-body problems ( http://www.amazon.com/Feynman-Diagrams-Many-Body-Problem-Physics/dp/0486670473 ) Page 21 (1.14) for ...
6
votes
4answers
789 views

Uncertainty Principle for Information?

I'm not familiar (yet) on how Information theory can be emerged/used in QM/QFT but I was thinking about this question: While we have Heisenberg uncertainty principle on measuring coupled observables, ...
2
votes
3answers
255 views

Zero Point Fluctuations

The total energy of a mode in a quantum mechanical resonator is given by $E_n ~=~ (n+ 1/2)hf$ where $n$ is the number of modes. So when there are no modes or vibrations, i.e. $n=0$, the energy is ...
6
votes
1answer
256 views

Is it possible to make statements about bosonic/fermionic systems by taking the limit $\theta\to \pi$ or $\theta\to 0$, of an anyonic system?

One might naïvely write the (anti-)commutation relations for bosonic/fermionic ladder operators as limits $$ \delta_{k,\ell} = \bigl[ \hat{b}_{k}, \hat{b}_{\ell}^\dagger \bigr] = ...
5
votes
1answer
477 views

Basis transformation between eigenstates of harmonic oscillators with different frequency

Given two harmonic oscillators with frequencies $\Omega$ and $\Omega'$, the eigenstates themselves are exactly known. Let's call them $\Psi_n$ and $\Psi'_n$. Is there a compact expression for the ...
3
votes
1answer
361 views

How do eigenstates of harmonic oscillators with different frequencies compare?

Suppose I have a harmonic oscillator with frequency $\Omega_1$ and another one with frequency $\Omega_2$. Is there a simple relationship between the eigenstates of the two? Especially, how would the ...
8
votes
4answers
3k views

Difficulties with bra-ket notation

I have started to study quantum mechanics. I know linear algebra,functional analysis, calculus, and so on, but at this moment I have a problem in Dirac bra-ket formalism. Namely, I have problem with ...
1
vote
0answers
112 views

Wigner $3j$ symbols

I am trying to determine the expansion that requires using $3j$ symbols; however, I am running into some conceptual snags. First, the expansion produces symbols that have m's that do not agree with ...
21
votes
6answers
1k views

Is the density operator a mathematical convenience or a 'fundamental' aspect of quantum mechanics?

In quantum mechanics, one makes the distinction between mixed states and pure states. A classic example of a mixed state is a beam of photons in which 50% have spin in the positive $z$-direction and ...
2
votes
2answers
8k views

Minimum possible Kinetic Energy of a confined electron

The problem is this: Consider an electron confined in a region of nuclear dimensions (about 5 fm). Find its minimum possible kinetic energy in MeV. Treat this problem as one-dimensional, and ...
0
votes
1answer
321 views

Inhomogenous Schrödinger equation

Please help me out in solving this inhomogeneous Schrödinger equation in cylindrical co-ordinates [You may suggest if I have to go for mathematics]: $$ \ddot R + \frac1r\dot ...
0
votes
1answer
400 views

Spring-mass physics homework question [closed]

I've been having trouble with my physics homework. The problem is: You may have measured the properties of a simple spring-mass system in the lab. Suppose you found ks = 0.9 N/m and m = 0.01 kg, ...
9
votes
4answers
1k views

What does a de Broglie wave look like?

What does a de Broglie wave look like? Are de Broglie waves transverse or longitudinal? Can they be polarized? What about the de Broglie wave of a ground state neutral spin-zero Helium 4 atom? ...
9
votes
2answers
1k views

What does the Canonical Commutation Relation (CCR) tell me about the overlap between Position and Momentum bases?

I'm curious whether I can find the overlap $\langle q | p \rangle$ knowing only the following: $|q\rangle$ is an eigenvector of an operator $Q$ with eigenvalue $q$. $|p\rangle$ is an eigenvector of ...
6
votes
1answer
215 views

Can closed loops evade the spin-statistic theorem in 3 dimensions?

The famous spin-statistics result asserts that there are only bosons and fermions, and that they have integer and integer-and-a-half spin respectively. In two-dimensional condensed matter systems, ...
5
votes
2answers
1k views

Matter waves - DeBroglie's relations

I am currently studying from Modern Physics for Scientists and Engineers by Taylor et al. They derive the DeBroglie relation $p=h/\lambda$ from setting mass $m=0$ in the energy-momentum relation ...
5
votes
1answer
346 views

Boundary conditions from single-valuedness of spherical wavefunctions

This question is a follow-up to David Bar Moshe's answer to my earlier question on the Aharonov-Bohm effect and flux-quantization. What I forgot was that it is not the wavefunction that must be ...
3
votes
2answers
312 views

Diagram-like perturbation theory in quantum mechanics

There seems to be a formalism of quantum mechanics perturbation that involve something like Feynman diagrams. The advantage is that contrary to the complicated formulas in standard texts, this ...
2
votes
1answer
660 views

Theoretical treatment of Hydrogen bond?

I would like to understand how the Hydrogen bond can be described through the Schroedinger equation. I don't need numerical methods that one uses them to simulate it, rather I need its treatment from ...
0
votes
2answers
619 views

When and how do you represent a two body state as a tensor product?

I have read that in quantum mechanics, compound systems are constructed as tensor products. But on page 177 of Griffith, for example, a two body wavefunction is introduced as Psi ...
2
votes
2answers
2k views

Quantum phyics project for a high schooler [duplicate]

Possible Duplicate: Study Quantum Physics I am a high schooler who is interested in physics and mathematics, and I have a kind of 'high-school thesis' coming up in a year and a half or so. ...
5
votes
3answers
444 views

Why possibility for X-ray to excite inner electrons higher than outer electrons?

It seems X-ray absorption spectroscopy is usually ascribed to the interation between photons and inner electrons. Does it mean inner electrons are much preferred by X-ray photons to outer electrons? ...
53
votes
8answers
4k views

Is there a symmetry associated to the conservation of information?

Conservation of information seems to be a deep physical principle. For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory. We may wonder if there is an underlying ...
5
votes
4answers
234 views

Is there a quantum state for a large system

My understanding of quantum mechanics is that the state of a system is represented by a vector in multidimensional complex vector space. Is there, in principal, a state vector that represents a large, ...
0
votes
2answers
126 views

Wave function of IQH and FQH electrons

What are the wave functions of the ground state of Integer Quantum Hall (IQH) and Fractional Quantum Hall (FQH) electrons?
5
votes
3answers
509 views

Why we use $L_2$ Space In QM?

I asked this question for many people/professors without getting a sufficient answer, why in QM Lebesgue spaces of second degree are assumed to be the one that corresponds to the Hilbert vector space ...
1
vote
1answer
78 views

How is a qubit realized in a cavity?

Considering a single photon in a cavity, how is a qubit realized in this setup? How is the qubit $|0\rangle$ or $|1\rangle$ manipulated? I.e. how are the transitions $|0\rangle \to |1\rangle$ and ...
4
votes
1answer
1k views

What is the spin rotation operator for spin > 1/2?

For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form: ...
3
votes
1answer
308 views

Simulating quantum network of harmonic oscillators

Let's say that I have a system of $n$ particles $p_1,\ldots,p_n\in\mathbb{R}^3$ (where $n$ here is on the order of 10,000). Furthermore, suppose we have a graph $G=(V,E)$ describing some network, ...
3
votes
2answers
288 views

Probability wave speed of dispersion and interference

I'm a layperson learning about quantum mechanics and probability waves. My understanding is that the probability wave for the position of a particle disperses throughout all of the universe. I have ...
5
votes
1answer
522 views

Many-worlds: Where does the energy come from?

With regard to the theory that each time a wave function collapses the universe splits so that each possible outcome really exists - where does all the energy required to create all the new universes ...
5
votes
3answers
461 views

Rationale for writing wave function as product of independent wave functions

When solving Schrödinger's equation for a 3D quantum well with infinite barriers, my reference states that: $$\psi(x,y,z) = \psi(x)\psi(y)\psi(z) \quad\text{when}\quad V(x,y,z) = V(x) + V(y) + V(z) = ...
2
votes
1answer
196 views

constraint on scaling dimension

How can we show that for any scalar operator $\Delta\geq1$ (where $\Delta$ is the scaling dimension)? Where can I find a reference for reading where it comes from?
-2
votes
1answer
69 views

Assuming collision , are there fundamental forces associated with absorbtion?

I just learned that strong and weak nuclear forces relate to decay/emission. I know absorbtion depends on Energy levels(QM) and heat(thermodynamics , kinetic energy , entropy) and E = gamma mc^2 ( ...
12
votes
4answers
1k views

Is the statistical interpretation of Quantum Mechanics dead?

I'm sure this question is a bit gauche for this site, but I'm just a mathematician trying to piece together some physical intuition. *Question:*Is the statistical interpretation of Quantum ...
4
votes
4answers
468 views

Does entropy decrease through measurement?

For an electron in its rest frame, we have an entropy $$ S = \log 2, $$ which comes from the 2 possible spin directions along z-axis. If the measurement $S_z$ changes its state to $\left| + ...
3
votes
1answer
544 views

Matrix order in Dirac equations

The trace of matrix is always sum of its eigen values , which can be seen if $\hat{U}$ transforms the matrix $\alpha_i$ into it's diagonal form . $$ \begin{pmatrix} A_1 & 0 & \cdots & 0 ...
4
votes
2answers
336 views

when photons can be trapped in a cavity and manipulated. How they can be observed without being destroyed?

An observer is anything that can cause a wave function to collapse. That is an interpretation of wave function collapse (usually referred to as the measurement problem). Now, when can photons be ...
3
votes
3answers
660 views

Disproving a refutation of quantum mechanics (QM) via a calculation of the ground state of the helium atom

This website http://www7b.biglobe.ne.jp/~kcy05t/ appears to refute Quantum mechanics using some proof. An important paper involved is this 'Calculation of Helium Ground State Energy by Bohr's ...
1
vote
3answers
566 views

Propagators and Probabilities in the Heisenberg Picture

I'm trying to understand why $$\Bigl|\langle0|\phi(x)\phi(y)|0\rangle\Bigr|^2$$ is the probability for a particle created at $y$ to propagate to $x$ where $\phi$ is the Klein-Gordon field. What's ...
0
votes
0answers
153 views

Dilatations in non-relativistic QM and operator tranformation

I was looking at a QM textbook exercise dealing with dilatations, the transformations are $x \rightarrow x' = \lambda x$ transforming $|\psi\rangle$ into $|\psi'\rangle = ...
1
vote
2answers
843 views

The Heisenberg uncertainty principle: Interpreting $\Delta p$, $\Delta t$, etc

(1) I have a textbook question that states the following: An electron has a speed of 500 m/s with an accuracy of 0.004%. Calculate the certainty with which we can locate the position of the ...
8
votes
5answers
625 views

Distinguishing identical particles

I've been going through Shankar's Principles of Quantum Mechanics. In the section of the system of identical particles, he uses an example of billiards to illustrate the difference between identical ...
2
votes
2answers
648 views

Non-commuting operators can't share any eigenvector

In an introductory Quantum Mechanics textbook, I found the following statement: For two Hamiltonians $H$ and $H'$, non commuting with each other, but commuting with the same group of translations ...