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
47 views

Plane Wave Solutions to the Majorana Equation with Zero Momentum

My question concerns the plane wave solutions to the Majorana equation. First, recall the Dirac equation: $$(i\gamma^\mu \partial_\mu-m)\psi=0$$ I suggest a solution in the form of a plane wave with ...
0
votes
1answer
44 views

Allowed Wave Functions of System

Given a single-particle system with Hamiltonian $H$, what constraints can be put on the wave function at a particular point in time $\psi(x)$? Of course $\psi(x)$ must obey boundary conditions given ...
0
votes
0answers
43 views

How to find the minimum value of potential in QM?

In MIT problem sets I followed a solution of an exercise which focuses on odd-parity energy eigenstates in finite square well. The point of problem is how to know or find the minimal value of ...
1
vote
1answer
22 views

Do any elements form stable doubly-charged negative ions?

It is perfectly possible for an atom - particularly on the electronegative end of the periodic table to form negatively-charged ions by attracting an electron, and these species can be stable, ...
3
votes
2answers
107 views

If a quantum state is pure why are its observables still probabilistic?

As I understand it, a pure quantum state is one that can be represented as a ket $\lvert\psi\rangle$ in a Hilbert space, and it contains all the information about the state of the system. As such, we ...
0
votes
0answers
29 views

Spin Orbit Coupling Hamiltonians

I am really struggling with something fundamental. I keep coming across two versions of the hamiltonian for spin orbit coupling: $H_{soc}=\frac{\mu_B}{2c^2}(v \times E) \cdot \sigma $ $\mu_B =$ ...
4
votes
1answer
66 views

How could we describe the electric bound state like hydrogen by QED? [duplicate]

We can solve the Schrodinger equation for the Hamiltonian operator from the classical Hamiltonian of hydrogen bound state, consisting of proton and electron attracting each other electrodynamically, ...
-1
votes
1answer
46 views

Deriving eigen values of $\hat{N}$

So let's say we have an operator $\hat{a}$ (ladder operator), where $\left[\hat{a},\hat{a}^\dagger\right] = 1$, and $\hat{a}^2 |\phi\rangle = 0$. How do I show that the eigenvalues of ...
4
votes
3answers
102 views

Same quantum states represented in different basis

In literature on an introduction to quantum mechanics which I am working through, there is a section which explains that a vector has different representations based on the basis you choose and then ...
-1
votes
1answer
47 views

quantum entanglement and its application in migratory birds [closed]

Explain the concept of quantum entanglement.Also explain its application in migratory birds. i know that it also has a relation with the magnetic field of the earth.
1
vote
0answers
65 views

Quantization of non-variational systems?

In undergraduate courses the introduction to Hamiltonian mechanics usually starts from a Newtonian view point. One has equations of motions of the form (not sure if it is ok to use covariant notation ...
3
votes
2answers
135 views

Schrödinger equation in momentum space

In literature on an introduction to quantum mechanics which I am working through, there is a section which explains that a vector has different representations based on the basis you choose. It then ...
3
votes
1answer
70 views

What is a weak value really?

There have been a lot of recent experiments performing weak measurements. Some of the conclusions seem to be quite surprising (e.g. this paper) and there is still debate if the weak measurement is ...
1
vote
1answer
57 views

Mathematical proof of Bohr's complementarity principle

Complementarity principle, in physics, tenet that a complete knowledge of phenomena on atomic dimensions requires a description of both wave and particle properties. Depending on the experimental ...
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
56 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
28 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
181 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
306 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.