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)

3
votes
1answer
118 views

How is Lippmann-Schwinger equation derived?

I'd like to know the derivation of Lippmann-Schwinger equation (LSE) in operator formalism and on what assumptions it is based. I consulted the Ballentine book as advised in this Phys.SE post, but I ...
6
votes
1answer
76 views

7/2 versus 9/2 for diatomic heat capacity

Question I calculated the classical heat capacity of a diatomic gas as $C_V = (9/2)Nk_B$, however the accepted value is $C_V = (7/2)Nk_B$. I assumed the classical Hamiltonian of two identical atoms ...
0
votes
1answer
31 views

Simultaneous measurement for quantum entanglement

In the simple example that we measure the spin of two entangled particles, we measure one to have spin up so we know the other has spin down. If we could (theoretically) measure both particles at the ...
0
votes
2answers
76 views

Do black holes violate the Uncertainty Principle?

If black holes have mass but no size, does that imply zero uncertainty in position? If so, what does that imply for uncertainty in momentum?
3
votes
0answers
117 views

What is the Copenhagen interpretation of quantum field theory?

I am most interested in interpretational differences due to the fact that quantum field theory is relativistic while quantum mechanics is not. By "Copenhagen interpretation" I mean a minimal ...
1
vote
1answer
43 views

Quantum force and classical limit

Today my physicist friend told me about Bohmian mechanics as an alternative way of looking at QM. He told me that in Bohmian mechanics the wave function gives rise to another fundamental force (the ...
0
votes
0answers
28 views

Photon's behavior from 1-dimensional realm to 3-dimensional realm

I know that photon's behavior can be fully analyzed (or at least a solid theoretical explanation is present, see molecular QED book) when the photon is emitted and absorbed by same dimensional ...
0
votes
2answers
94 views

How does Lorentz invariance make $(\Psi_0,J_{\mu}\Psi_0)$ vanish?

Right before equation (10.4.7) in Weinberg's volume 1 on quantum field theory, he said $(\Psi_0,J_{\mu}\Psi_0)$ vanishes due to requirement of Lorentz invariance. As I understand, this term is a ...
0
votes
0answers
28 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
104 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
15 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
45 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
43 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
29 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
49 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
59 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
377 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
57 views

Why do electrons occupy in discrete energy states?

Why can't there be any continuous energy band in an atom?
0
votes
1answer
56 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
300 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
64 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
41 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
57 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
53 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
858 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
45 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
66 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
56 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
209 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
57 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
46 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
172 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
93 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
96 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
42 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
111 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?