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
4answers
89 views

What is $V(x)$ in Schrödinger's equation?

In the time-independent Schrödinger equation it is stated that $$-\frac{\hbar^2}{2m}\frac{d^2\psi(x)}{dx^2}+V(x)\psi(x)=E\psi(x)$$ And it is common to give $V(x)$ some standard "forms": the infinite ...
1
vote
1answer
26 views

Adjoint momentum Dirac equation

So we have the commonly quoted momentum space version of the Dirac equation and the adjoint Dirac equation: $$ (\gamma^{\mu}p_{\mu}-m)u=0 $$ Often, we are asked to show that the adjoint momentum ...
0
votes
1answer
25 views

Reflection in Finite Square Wells

For a Finite Square Well where we have a wavefunction $\psi(x)$ which is an energy eigenfunction with eigenvalue $E = 2V_0$ in the following potential: $V(x) = \begin{array}{ll} 6V_0 ...
0
votes
1answer
28 views

Nodes for a hydrogen atom probability?

It is said that the wave function $\psi_{n,m,l}$ has $n-1$ nodes; $n-l-1$ from the radial part of the wavefunction and $l$ from the angular part. However, the probability of finding a particle at a ...
0
votes
1answer
40 views

Wavefunction of a system of particles

A three-dimensional volume $V$ contains a certain number $N$ of electrons and they can't escape the volume $V$. Assume for simplicity that the potential $\mathcal{V}(\mathbf{r})$ is zero in all the ...
0
votes
2answers
55 views

Linear Combinations of Energy Eigenfunctions in 1D

Given that a particle is in a state defined by the wavefunction: $$\Psi (x,t) = \psi_0(x)e^{-iE_0t/\hbar}+\psi_1(x)e^{-iE_1t/\hbar}$$ where $\psi_0(x)$ and $\psi_1(x)$ are the energy eigenfunctions of ...
13
votes
4answers
2k views

What is a wave function in simple language?

In my textbook it is given that 'The wave function describes the position and state of the electron and its square gives the probability density of electrons.' Can someone give me a very ...
0
votes
1answer
27 views

Given any two quantum states and the information that the system is in one of these two states

Given any two quantum states and the information that the system is in one of these two states, one cannot reliably devise a single measurement which could determine with certainty which state the ...
0
votes
3answers
83 views

Quantum computing entanglement dimensions question

While trying to understand the basics of how quantum computers work, I recently read this statement. "...consider that single-qubit states can be represented by a point inside a sphere in ...
0
votes
0answers
14 views

What's the difference between an exciton and a geminate pair?

In the context of organic solar cells, electron-hole dissociation is sometimes mentioned with regard to excitons (refs 1, 2) and sometime with regard to geminate pairs (refs 3, 4). Also, exciton ...
1
vote
0answers
16 views

Wigner-Eckart theorem and Van Vleck paramagnetism

Using the Wigner-Eckart theorem, we can express the matrix elements of Langevin's paramagnetic Hamiltonian $L_z + g_S S_z$ using only the quantum numbers of the total angular momentum, $J$ and $m_J$, ...
3
votes
1answer
37 views

Relation between the electromagnetic wave and quantum wavefunction

I have been thinking about this for a while. I think I misunderstood something about the basics of quantum waves. Let's look at light diffracted in conditions similar to the double slit experiment. ...
0
votes
0answers
24 views

Showing the transmission coefficient is valid

In a semiconductor device, electrons accelerated through a potential difference of 7V attempts to tunnel through a barrier of width 0.5nm and height 10V. Assume the potential is zero outside the ...
1
vote
2answers
42 views

Quantization of the Hamiltonian of a particle in a uniform magnetic field

If a particle of mass $m$ and charge $q$ is subject to a uniform magnetic field and if we have a vector potential $\mathbf{A}$ then we know that classically the dynamics of the particle will be ...
-1
votes
2answers
38 views

Degrees of degeneracy of energy values

Let us consider the harmonic oscilator in three dimensions whose hamiltonian is: $$H = \dfrac{1}{2m} \mathbf{P}^2+\dfrac{m\omega^2}{2 }\mathbf{R}^2.$$ The nicest way to solve the eigenvalue equation ...
0
votes
0answers
35 views

Lagrangian derivation of Thomson scattering cross section (ie photon-electron)

Does anyone know a quick way to obtain the classical Thomson scattering scattering cross section (for photons scattering on electrons) from quantum mechanics/quantum field theory, avoiding the lengthy ...
7
votes
2answers
116 views

Do bosons and fermions produce the same interference pattern in a double slit experiment?

I have read that when bosons interfere they do so by adding the probability amplitudes, then I read that when fermions interfere they do so by subtracting the probability amplitudes. The usual double ...
1
vote
0answers
21 views

Why does the electron lose energy? [duplicate]

We all know that when a photon impacts on an electron it delivers all its energy to the electron and the electron's energy increases and it goes to a higher-energy state -- meaning farther from the ...
1
vote
0answers
49 views

Calculating Natural Broadening of Emission Lines

I'm trying to demonstrate the small effect of Natural Broadening as compared to other types of broadening (Doppler, Stark, van der Waals, etc.) and my calculations don't match the accepted values. My ...
3
votes
1answer
66 views

Practical Calculation of Geometric Phase

I'm a graduate student working in the field of quantum chemistry, specifically in the field of non-adiabatic dynamics of molecular systems. I've run into a slight problem in a project that I've ...
1
vote
0answers
35 views

Lippmann-Schwinger equation and time dependence

Consider the Lippmann-Schwinger equation (LSE) $$ |\psi\rangle = |\phi\rangle + \hat{G}_0(\epsilon) \hat{V} |\psi\rangle \tag{1}$$ where $\hat{G}_0(\epsilon) = \frac{1}{\epsilon - \hat{H}_0 + ...
1
vote
0answers
63 views

Why not measure the velocity of a quantum particle by $\frac{\Delta \vec{x}}{\Delta t}$

Why is it not possible in quantum mechanics to measure the velocity (and thus momentum) of a particle just by two position and time measurements and get it approximately by $$ \vec{v} = ...
0
votes
0answers
27 views

How can absorbtion of a photon in an atom take place? [duplicate]

I will come back to a question posed here and the comment given by John Rennie: If the photon energy doesn't match an allowed transition energy it won't be absorbed and won't excite any transition. ...
0
votes
1answer
32 views

How does one determine orbital configurations in multi-electron atoms?

When we measure absorption/emission spectra for hydrogen-like atoms, we can point to a particular line/energy level and say "Aha! That's almost exactly the $A\rightarrow B$ transition that we ...
0
votes
0answers
18 views

Field Coherent State relationship to annihilation operator

I am trying to show that $|\Psi_{\lambda\bar{n}}> = \sum c_{\lambda\bar{n}m}\exp(-i(n+\frac{1}{2})\omega_\lambda t)|n_\lambda>$, where $c_{\lambda\bar{n}m} = ...
0
votes
0answers
13 views

Why self-quenching (aka concentration quenching) of fluorophores is possible?

In some cases, increasing the concentration of a fluorofore results in reduced fluorescence, due to self-quenching (aka concentration quenching). (source) On the other hand, self excitation supposed ...
1
vote
0answers
21 views

Particle in a $V(\rho)$ potential in cylindrical coordinates

Consider cylindrical coordinates $(\rho,\phi,z)$ and consider a particle with a potential energy $V(\rho)$. If we write the Hamiltonian operator in these coordinates we find that $$H = ...
4
votes
1answer
194 views

Regular solution vs irregular solution

My Quantum Mechanics textbook (John S. Townsend's A Modern Approach to Quantum Mechanics) mentions regular solutions and irregular solutions. It claims that regular solutions (at the origin) to the ...
0
votes
1answer
22 views

Uncoupled and coupled bases for electrons in hydrogen atom?

I'm given that for an electron in a hydrogen atom, $L=2$ and $S=1/2$ (quantum numbers associated with $L^2$ and $S^2$). I'm also given that for the uncoupled representation, the basis function is ...
7
votes
3answers
180 views

What do the wave functions associated to the Fock states of each mode of a bound state system mean?

$\renewcommand{\ket}[1]{\left \lvert #1 \right \rangle}$ Consider a string of length $L$ under tension and clamped on each end. This system is described by the wave equation and has a set of modes. ...
1
vote
0answers
47 views

Heisenberg theory of uncertainty

I was watching a video on YouTube about uncertainty theory of Heisenberg it said that there is a relation between momentum (multiple of mass and speed) and wave length. And the relation is that if ...
1
vote
0answers
36 views

Can Bose-Einstein Condensates reflect gravitational waves?

This is a question based on the paper by Raymond Chiao in 2002 where it is stated: One of the conceptual tensions between quantum mechanics (QM) and general relativity (GR) arises from the clash ...
0
votes
1answer
27 views

Expressing Spin State |r> As Linear Superposition of |u> and |d>: Basic Linear Algebra?

Background This question, from Quantum Mechanics: The Theoretical Minimum started with the following assumption(?) $$|r\rangle = \frac{1}{\sqrt 2}|u\rangle + \frac{1}{\sqrt 2}|d\rangle$$ I'm now ...
0
votes
0answers
26 views

Construct any Hamiltonian that is the linear combination of existing constructable Hamiltonians

In the paper Quantum Computation over Continuous Variables, it states that since $$e^{iAt}e^{iBt}e^{-iAt}e^{-iBt} = e^{-[A,B] t^2} + O(t^3)$$ when $t\rightarrow 0$, if one can apply a set of ...
8
votes
2answers
300 views

The Origins of the Second Quantization

I've been studying quantum theory for a while now and have a number of closely related questions that are not giving me any peace. I am not sure if such a long format is appropriate here, but I'd like ...
1
vote
2answers
94 views

Representation of the states of a quantum system

Is it true that the states of a quantum system are represented by vectors in a Hilbert space? I've read something about "rays" and I'm confused.
-2
votes
2answers
63 views

Can a non-entangled qubit be teleported by entangling it?

Let's say I have a qubit that is not entangled in state $\psi$. I want to teleport this qubit by entangling it with another qubit but still getting $\psi$ back in the end. Is this possible, or would ...
4
votes
2answers
114 views

What exactly does No cloning mean, in the context of Quantum Computing?

I am trying to get an intuitive idea of how the No-Cloning theorem affects Quantum computation. My understanding is that given a qubit $Q$ in superposition $Q_0 \left| 0 \right> + Q_1 \left| 1 ...
0
votes
1answer
46 views

Multiple measurements and the any worlds interpretation

My question has some similarities to but also differs significantly from this question which was described in many of its answers as not being a quantum mechanical measurement and was I think, ...
0
votes
0answers
11 views

How does electrical current affect electronic band density?

When sending a current through a conductor, electrons in the valence band gain energy. What does that mean concretely? Are electrons excited uniformly, i.e. all electrons in the valence band gain ...
1
vote
0answers
10 views

Why singlet and triplet states are not mentioned when dealing with inorganic semiconductors or other heavy materials?

Singlet and triplet states get attention in organic materials (fluorescence, phosphorescence, upconversion). Why singlet/triplet states are never mentioned in the context of inorganic semiconductors, ...
0
votes
1answer
41 views

Why do bonds with positive and negative charges not collapse?

I previously believed that the reason positive and negative charges don't constantly attract until they collapse is due to a repulsive strong force at small distances. However, in a textbook by ...
0
votes
1answer
54 views

Single particle tunneling Hamiltonian

In reference to Problem 9, Chapter 2 in Modern Quantum Mechanics by JJ Sakurai, For a single particle tunneling in a 1D double well potential, with position eigenkets $\mid R\rangle$, $\mid ...
3
votes
2answers
116 views

When does the world split in MWI

I've been reading Eliezer Yudkowsky's blog post regarding decoherence and many worlds, and although he is not a physics but a strong proponent of MWI, I can basically see why he feels that MWI is a ...
1
vote
1answer
58 views

QM sytem with eigenvalues of the form $f(m*n)$ and prime number gap spectrum

Depending on the dimension and the symmetry and form of the potential, the energy eigenvalues of a quantum mechanical system have different functional forms. Eg. The particle in the 1D-box gives rise ...
1
vote
3answers
98 views

Precedence and quantum entanglement: The Alain Aspect experiment in spacetime

Recall that the spin components of a spin-entangled pair do not exist until one of the pair undergoes quantum observation, at which time both of the pair immediately obtain quantum random opposing ...
0
votes
0answers
26 views

Transformation applied to system without symmetry

Imagine we have a central potential which gives us the Hamiltonian of the form: $$\hat H=-\frac{\hbar^2}{2m} \nabla^2 +V(r)$$ In general this is not symmetric under translation. But let us say that I ...
3
votes
1answer
47 views

Is QC with Superpositioned Quantum Gates any different than normal Quantum Computation?

This might be more appropriate for theoretical CS stackexchange, but it feels sufficiently low level to be relevant here. Consider the following thought experiment: I have a Quantum FPGA, it is a ...
1
vote
1answer
102 views

Three dimensional isotropic harmonic oscilator Hamiltonian

Let us consider the Hamiltonian for the isotropic three dimensional harmonic oscilator: $$H = \dfrac{\mathbf{P}^2}{2m}+\dfrac{m\omega^2\mathbf{R}^2}{2},$$ where $\mathbf{P}$ and $\mathbf{R}$ are the ...
0
votes
1answer
22 views

Why does parahydrogen have a lower energy than orthohydrogen?

I found this on the wikipedia page on spin isomers of hydrogen: Parahydrogen is in a lower energy state than is orthohydrogen. It seem almost like it is obvious but I am having trouble reasoning ...