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)

0
votes
0answers
30 views

Weak measurement and weak value

The concept of weak measurements (and weak values) have become popular in Quantum information community, as I can see quite a few papers in arXiv. Since I am from Mathematical background (and the ...
6
votes
2answers
107 views

What state the wave function collapses into after an inaccurate measurement?

I'm watching MIT online lectures Quantum Physics I (roughly from one hour mark in the video). The lecturer explains wave functions that describe "Stationary States" that consist of a single energy ...
0
votes
1answer
25 views

Is there any restriction on the ability to measure the full quantum state of a system without inducing backaction?

Suppose an arbitrary quantum system is in the state $ \mid \Psi \rangle $, which may or may not be a function of time. An initially ignorant obsevrer would like to figure out what $ \mid \Psi ...
0
votes
0answers
16 views

Can we use Variational Monte Carlo for degenerate cases?

Consider Simple Example of Bose-Hubbard model $$H=-J\sum\limits_{<i,j>}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1) . \tag{1}$$ We can solve this Hamiltonian by Variational ...
0
votes
1answer
48 views

Physical significance of momentum eigenfunction

In an introductory textbook of Quantum Mechanics, I found the momentum eigenfunction in position space to be given as Ne^ipx/h. Where N is the normalization factor and i is root of -1. I don't ...
0
votes
0answers
47 views

What is this normalization principle called in quantum mechanics?

I searched all over the web about this: $$\left|\Psi\right> = ...
-2
votes
0answers
16 views

Why is $|a,b>+ |-a,-b>$ annihilated by the ladder operator $E_{a,b}+ E_{-a,-b}$, but no other?

Ladder operators act on states $|a,b>$ by $$E_{c,d}|a,b> = |a+c,b+d> $$ Other possible ladder operators in my example are $E_{-a,b}$, $ E_{a,-b}$ or some linear combination of them. ...
0
votes
1answer
36 views

Why does a measurement on one qubit force another one into a given state in Simon's algorithm?

This comes from trying to understand the "Simon's algorithm". So we have a set of $2^n$ kets $|x_i >$ one each for $i \in \{0,1\}^n$. Each $x_j \in \{0,1\}^n$. And we have the further constraint ...
0
votes
1answer
42 views

Would infinite material cause a black hole?

If you have an infinite amount of any material(That doesn't have a critical mass to have nuclear reactions), would this matter form massive black holes that condense into an infinite black hole? Two ...
0
votes
1answer
45 views

Unitary change of X basis, shankar, quantum mechanics 7.4.9

I'm currently working through Shankar's Quantum Mechanics and am stuck on one of his exercises. In Exercise 7.4.9 Shankar would like us to show $$|\tilde{x}\rangle = \exp(ig(x)/\hbar) |x\rangle$$ ...
0
votes
1answer
30 views

How are resistivity and tunneling related?

If we consider a sandwich with three nanometric layers: conductor-insulator-conductor and apply voltage (lower than breakdown voltage) from both sides tunneling will occur. Is tunneling dependent on ...
1
vote
1answer
53 views

Angular Momentum Operators - Commutation Relations

I was going over past PGRE exam questions, and came across this one. The components for the angular momentum operator $\mathbf{L}=(L_x,L_y,L_z)$ satisfy the following commutation relations. ...
2
votes
0answers
60 views

About the definition of the spin current

People have been talking about the spin current for a while. But there is a fundamental problem. Unlike charge, or mass, spin is not conserved. Let us take the 1d spin-1/2 Heisenberg chain as an ...
12
votes
6answers
385 views

Has a double slit experiment ever been done using a track chamber or even contemplated?

I tried searches and the question has been posed in other fora, but no experiment came up. Track chambers (cloud chambers, bubble chambers , time projection chambers, solid state detectors like the ...
0
votes
1answer
59 views

Why do electrons occupy in discrete energy states?

Why can't there be any continuous energy band in an atom?
0
votes
1answer
57 views

Beam splitter in Q.M. and C.M. - Formalism

In Q.M. the beam splitter is represented by the Hadamard transform (at least if the particle is in a state $|\Psi \rangle = \left( \frac{1}{\sqrt2} \right )(|0\rangle + |1\rangle)$ ) The Hadamard ...
1
vote
0answers
59 views

Does Quantum Mechanics need imaginary numbers? [duplicate]

In quantum mechanics, we assume wavefunctions are complex valued, and that probability amplitudes are given by the modulus of the wavefunction squared. This formalism can correctly explain ...
1
vote
7answers
308 views

Quantization vs. continuous energy levels

I still don't get what it means for atomic energy levels to be continuous or quantitized (incontinuous). Clearing this up will really help me. Also, can anyone tell me why energy levels in solids are ...
0
votes
1answer
66 views

Negative sign in rotation operator again

In Wikipedia's page on the rotation operator, section "In relation to the orbital angular momentum", they write $$ R(z,t) = exp((-i/h) \varphi L_z) $$ where $\varphi$ is the angle being rotated ...
0
votes
1answer
28 views

Compton scattering's frequency paradox

In Compton scattering, the wavelength difference of scattered radiation is measured as, as well as calculated by conservation of momentum: $\lambda - \lambda'={\frac{h}{mc}} (1-cos\theta)$ where ...
1
vote
1answer
42 views

ideally accurate measurement

In the address below http://en.wikipedia.org/wiki/Measurement_in_quantum_mechanics it's written: For pedagogic reasons, the measurement [in quantum mechanics] is usually assumed to be ideally ...
-3
votes
1answer
59 views

Eigenstates of sum of creation and annihilation operators

Does the operator $a+a^\dagger$ have eigenstates? If yes, what are they?
1
vote
1answer
54 views

Momentum uncertainty of free particle

I've read several Q&A's regarding free particles and the associated wave packet in this website, but found the answer to my question nowhere. It's OK to attribute a Gaussian wave packet to the ...
4
votes
2answers
859 views

Which theory explains the path of a photon in Young's double-slit experiment?

In Young's double-slit experiment, we know that a photon goes through either one of the slits but we don't know which one, and it ends up on a screen. I want to know which theory can predict to the ...
3
votes
1answer
49 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 ...
1
vote
1answer
71 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 ...
2
votes
2answers
69 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 ...
0
votes
1answer
57 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 ...
3
votes
3answers
211 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 ...
0
votes
1answer
58 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 ...
1
vote
1answer
72 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 ...
0
votes
0answers
52 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 $n$ ...
1
vote
0answers
30 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 ...
0
votes
5answers
114 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 ...
10
votes
1answer
175 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 ...
1
vote
0answers
96 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 ...
2
votes
2answers
97 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 ...
2
votes
0answers
35 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 ...
1
vote
1answer
45 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 ...
1
vote
1answer
61 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 ...
0
votes
0answers
19 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 ...
0
votes
4answers
114 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
votes
2answers
178 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 ...
1
vote
1answer
60 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 ...
-3
votes
1answer
63 views

Does new energy creation exist?

I know that basic physics states that energy cannot be created or destroyed, but why is that true? For example, one theory called Quantum Fluctuation states that 'normal' and anti energy is constantly ...
1
vote
0answers
60 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 ...
0
votes
2answers
45 views

Possible values of an observable are the eigenvalues of an operator

Ok, so I'm beginning to study quantum mechanics. For reference, the book I'm using is "Konishi-Paffuti/Quantum Mechanics-A New introduction". Now, I get that the quantum state of something (say, a ...
2
votes
0answers
50 views

Why we need to suppose the chemical potential is zero here?

I've been working on some statistical mechanics problems and one of them asks to compute the pressure with chemical potential zero of a boson gas whose particles do not interact and whose energies are ...
1
vote
0answers
77 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 ...
2
votes
1answer
53 views

Relation between Von Neumann entropy (and other entanglement measures) and thermodynamical entropy

Suppose I have a bipartite system (with Hilbert space $H = H_a \times H_b$) and the following state: $$\sigma = \sum_{n} \frac{e^{-\beta E_n}}{Z} \rho_n$$ where $Z = \sum_n e^{- \beta E_n}$ and ...