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
56 views

Can a photon excite an electron via the uncertainty principle?

An electron is trapped in an infinite well potential with a width of $\Delta x$. A photon of wavelength $\lambda $ < $\Delta x$ is fired at the electron and misses or rather they don't interact. ...
7
votes
5answers
811 views

Double-slit experiment: Difference between observing photon path and interference pattern?

This is something that has confused me whenever I read about the double-slit experiment. When the double-slit experiment is performed, I understand that the resulting pattern for the sequentially ...
2
votes
1answer
52 views

Smoothness of the energy levels of a generic Hamiltonian

Let us take an Hamiltonian $H(\xi)$ which depends on a set of parameters $\xi$, and assume that the matrix elements $h_{ij}(\xi)$ of the Hamiltonian are smooth complex functions of the parameters ...
2
votes
2answers
124 views

Proof that entanglement is independent of distance

I've already read this quite often but never seen a proof—maybe it's just so clear to physicists, but I'm not really sure how to prove it. Currently I'm pretty confused so the following might be ...
0
votes
2answers
33 views

How to express a convex function of a Hermitian operator in terms of its eigenvalues and eigenvectors?

The Hermitian operator $\hat O$ can be expressed as $$\hat{O}=\sum_i O_i|O_i\rangle\langle O_i|.$$ How to prove that a convex function $f(\hat O)$ can be expressed like $$f (\hat O)=\sum_i ...
2
votes
1answer
388 views

How can it be derived that particles described by the Dirac equation must have spin 1/2?

I am reading some lecture notes that unfortunately don't seem to be available online, but that are quite close in spirit in their treatment of the Dirac equation to Sakurai's "Advanced Quantum ...
1
vote
0answers
30 views

Corrections in Perturbation theory

Is there a way to construct a bound on the perturbative corrections to a problem in perturbation theory? For example, if I have the standard 1st order correction to the eigensolutions of a problem ...
1
vote
1answer
48 views

Hermitian conjugate of an antiunitary transformation

In quantum mechanics, one often considers symmetry transformations which are defined in terms of operators which do not change the norm of states in the Hilbert space. For the Wigner's theorem, this ...
0
votes
1answer
41 views

Probability Density of a freely falling body

The following question has been taken from David J Griffith's Intro to QM. This is not my homework! :D Suppose I drop a rock off a cliff of height $h$. As it falls, I snap a million photographs, at ...
0
votes
0answers
15 views

Repulsive component of intermolecular interaction

Intermolecular interaction mainly consists of 2 components: (a) Dipole vs dipole (permanent & induced), which is more likely to be attractive (b) Pauli exclusion, which is always repulsive The ...
0
votes
0answers
41 views

Are Landau levels always degenerate?

Solving the Landau problem, namely the quantum mechanical problem of a particle in a magnetic field leads to degenerate energy states, the famous Landau levels. My question consists of two parts. ...
3
votes
1answer
216 views

The dual role of (anti-)Hermitian operators in quantum mechanics

Hermitian (or anti-Hermitian) operators are of central importance in quantum mechanics in at least two different incarnations: Observables are represented by Hermitian operators on the quantum ...
2
votes
0answers
65 views

How to get Heisenberg Equation of Motion?

If a system Hamiltonian is given by, $$ ...
0
votes
1answer
68 views

Dirac Eqn: why separate operators

At some point Dirac writes: (OpA)(OpB)Y = 0 where OpA and OpB are those two brackets that differ only in the sign of m, then he deduces: (OpA)Y = 0 OR (OpB)Y = 0 (or is that AND). I don't get ...
2
votes
0answers
46 views

Amplitude for a string to propagate from one point to another

In Zwiebach’s book sections 12.6 and 12.7 interesting aspects of the wave function of the string are discussed. In order to introduce my question first recall what happens with the relativistic ...
-1
votes
0answers
27 views

Electron wave function seen in Quantum Cascade Laser?

http://sciencequestionswithsurprisinganswers.org/images/qcllevels.gif How did they observe and take a picture of the electron wave function without collapsing it? Does this prove that the wave ...
1
vote
1answer
42 views

Relativistic probability amplitude of a particle to be in certain position

In the book “The story of spin” by Tomonaga on page 110, it says They insisted that a concept like "the probability of a particle to be at $x$ in space" is meaningless for relativistic ...
-1
votes
1answer
57 views

How can i only shine/shoot one proton/electron per second? [duplicate]

I would like to test out the two slit experiment but only one electron or proton at a time.
1
vote
0answers
79 views

Does Digital Physics imply Heisenberg's Uncertainty Principle? [closed]

I made the following observation which led me to believe that perhaps Digital Physics implies Heisenberg's Uncertainty Principle: Consider Noether's Theorem, which states that space-translation ...
1
vote
0answers
29 views

Bounds on mixing strength of a quantum channel

Consider a quantum channel $E$ acting on a $d$ dimensional quantum state, with a Kraus representation $E(\rho)= \sum_{j=1}^{k}A_j\rho A^{\dagger}_j$ (where matrices $A_j$ satisfy ...
1
vote
3answers
68 views

Born Interpretation of Wave Function

I have just started Griffiths Intro to QM. I was studying Born's interpretation of Wave function and it says that the square of the modulus of the wave function is a measure of the probability of ...
1
vote
0answers
27 views

What are some of the failed experiments to determine electron's position? [closed]

One that I could think of is trying to observe it with the help of electromagnetic radiation which could tear apart the atom. I asked this because I want to know what sort of methods are used to ...
0
votes
0answers
42 views

Problems with Dirac's Principles of Quantum Mechenics

I have been having some trouble reading Principles of Quantum Mechanics by P.A.M.D. I think it all burns down into two aspects. 1) In the theory of representations, the notation is awfull when we ...
1
vote
1answer
79 views

canonical ensemble that is quantum mechanical and continuous?

I do not understand what the following statements from Wikipedia mean For a canonical ensemble that is quantum mechanical and continuous, the canonical partition function is defined as $$ Z = ...
2
votes
1answer
94 views

Why electron can not be found at some node locations in the infinite potential well?

Consider electron in an infinite potential well, studied in quantum mechanics. Position probability density of the electron is $$ P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ ...
0
votes
2answers
71 views

Postulates of Relativistic Quantum Mechanics

I have been reading this Phys.SE answer in order to clarify my doubts. It seems to me that he claims that the postulates are the same no matter if it is QFT, QM or whatever. But some books tell us ...
0
votes
1answer
50 views

Would time-dependent wave-functions be constrained by relativity?

Please pardon my beginners understanding. I was thinking about the wave function of a "free particle", $\psi(x,t)$, where $\psi(x,0)$ is the initial condition. Writing $\psi (x,t)$ as $\sum\limits_n ...
5
votes
1answer
72 views

Delocalization in the square root version of Klein-Gordon equation

In this Wikipedia article a relativistic wave equation is derived using the Hamiltonian $$H=\sqrt{\textbf{p}^2 c^2 + m^2 c^4}$$ Substituting this into the Schrödinger equation gives the square root ...
0
votes
1answer
20 views

What trajectory do particles follow in the two-slit experiment in Bohm-de Broglie theory

In Bohm de Broglie interpretation of QM particles have trajectories; in the classic two-slit experiment what trajectories do they follow, and how is the interferance pattern interpreted? Are ...
1
vote
2answers
68 views

Where does the factor of $x$ come from in this formula for expectation value?

Given the normalised ground-state wave-function: $$\Psi(x, t)=\begin{cases} \sqrt\frac{2}{d}\cos(\frac{\pi x}{d})e^\frac{-i\hbar\pi^2t}{2md^2} & \ \lvert x\rvert<\frac{d}{2}, \\ 0 & ...
4
votes
4answers
136 views

Isn't the 'slit' in a double-slit experiment also a wave?

I'm new to QM so excuse my naivety. I was watching an online MIT QM course that described the double-slit experiment (with electrons) when it occurred to me that I have a question. In the video, the ...
0
votes
1answer
26 views

When does electron capture occur and when does positron emission occur?

I’ve been told that electron capture occurs when there isn’t enough energy to produce a positron by beta plus decay. Exactly why is this the case? Why does it take more energy for positron emission ...
0
votes
0answers
31 views

Addition of two spins

In the addition of two spins, $S_1$ and $S_2$ show that operators $S_1^2$,$S_2^2$,$S_{1z}$,$S_{2z}$ can have common eigenkets, however, operators $S^2$ and $S_{1z}$ cannot have common eigenkets for ...
0
votes
0answers
43 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, ...
-1
votes
0answers
41 views

Why do the quantum numbers take the value they do? [duplicate]

Clearly $n$ can take any positive integer value. But what is the physics and maths behind $l=0,1,...,n-1$ and $m_l=-l,-l+1,...,l-1,l$? i.e. where do these ranges of values come from? (P.S. I know ...
0
votes
0answers
53 views

Quantum operators in classical mechanics [closed]

Have you noticed that if a quantum operator is applied to a classical Hamiltonian, it will yield something proportional to the time derivative of the observable of the operator applied? For instance: ...
0
votes
0answers
20 views

Cancelling waves and preservation of energy

In quantum physics, a particle is "defined" by a wavefunction. If you would take 2 particles with the same wavefunction, and negate one of them. They would cancel each other other out. Take for ...
1
vote
2answers
69 views

The observer experiment: quantum mechanics

If an observer is needed to see something, but it is an observer that causes a quantum wave function to "collapse" into a classical state, how could we tell that the quantum wave function even existed ...
9
votes
4answers
683 views

Is double-slit experiment dependent on rate at which electrons are fired at slit?

I am a mathematician and I am studying string theory. For this purpose I studied quantum theory. After reading Feynman's book in which he described the double-slit experiment (Young's experiment) I ...
1
vote
0answers
24 views

How is it possible to combine various techniques in cold atom experiments?

I’ve been reading about laser-trapped cold atoms (6Li in particular, which is a fermion) and was amazed at the number of things to keep track of in the experiments, just to gain that degree of control ...
4
votes
1answer
72 views

Does QFT prevent preparation of an entangled particle pair as in EPR experiment?

This is the claim Tommasini makes in Reality, Measurement and Locality in Quantum Field Theory:"Two spin $1/2$ particles, A and B, are created in coincidence in a spin-singlet state, and are detected ...
2
votes
1answer
93 views

Prove: $A$ and $B$ commute, therefore functions $f(A)$ and $g(B)$ will always commute with one another [closed]

How do I / can I actually prove the relationship $[a,b]=0 \Rightarrow [f(a),g(b)]=0$ for all functions $f,g$. I'm asking because the following sentence in the solution to my quantum mechanics ...
-4
votes
0answers
35 views

Why do atoms oscillate? [closed]

We say, atoms are in constant motion. The question is why they are in motion. I think they are continuing the motion because there is no frictional force to decay the motion. But what causes the ...
1
vote
0answers
85 views

How can all quantum measurement statistics be seen just as projective measurements on pure states?

Let $\rho$ be the density matrix for a system and let the POVMs be $\{E_m\}$ such that $\sum_i {E_m} = I$. The probability of getting the outcome $m$ is $\operatorname{Tr}(E_m \rho)$. The source I ...
-4
votes
0answers
32 views

Is communication of the wavefunction via quantum entanglement possible?

Assume two particles are entangled and separated by an arbitrary distance. Particle 1 is in a potential well of width w1. If I'm not mistaken, the wavefunction of Particle 2 correlates to the ...
0
votes
0answers
44 views

Why does not the bare interaction potential appear in the Bogoliubov theory?

They use some effective potential defined by the s-wave scattering length, but not the bare atom-atom interaction $V(r)$. Why? It is standard practice in second quantization to use the bare ...
0
votes
0answers
28 views

Solutions to time-independent Schrödinger's equation with symmetrical (even) potential [duplicate]

A problem from Griffith's Introduction to Quantum Mechanics asks to prove the following: Given a symmetric potential $V(x)$ $(=V(-x))$, the solutions to the time-independent Schrödinger's equation ...
2
votes
2answers
60 views

unitary transformation in quantum mechanics

What two arbitrary states in the same Hilbert space can be connected through an unitary transformation? And how to construct the unitary transformation? Whether is there a general answers for these ...
0
votes
5answers
157 views

Where does particle borrow energy from to tunnel?

Where does particle borrow energy from to tunnel? It is implied that particle can borrow energy and leaped over to the other side wherever that is, the shorter the gap the more energy it borrows my ...
0
votes
1answer
47 views

physical meaning of dimensionless parameter

What does it mean when there is nor not a dimensionless parameter in my model? In quantum harmonic oscillator, we don't have dimensionless parameter while in hydrogen atom case we have one which is ...