All Questions
Tagged with computational-physicswavefunction
39 questions
0votes
1answer
111views
Why, if the potential is different from the Coulomb one, but has spherical symmetry, the eigenvalues of the system are non-degenerate?
I have found the eigenvalues of the following systems: $H=-\frac{1}{2}\Delta+V_1$ and $H=-\frac{1}{2}\Delta+V_2$, using NDEigensystem by Wolfram Mathematica. In the ...
- 233
0votes
0answers
37views
Does the phase of an electronic ground state wavefunction matter in a numerical calculation?
Does the phase of wavefunction matter in a numerical calculation? Recently, I was trying to solve a simple model system using numerical grid-based methods and saw that the phase of the ground state ...
- 362
1vote
0answers
107views
How to expand the existing basis set so that it becomes more complete?
This Mathematica.SE question https://mathematica.stackexchange.com/q/284679/ is physical too, so I have decided to duplicate it here. I have a set of anisotropic gaussian basis set which describes the ...
- 233
1vote
1answer
327views
Numerical solutions to 1D Schrodinger equation suggest degenerate energy eigenvalues, though this is supposedly disallowed
I am working on solving the time-independent Schrodinger equation using the method of finite differences. This approach has been discussed previously on this site (here, for instance). My code is ...
- 694
0votes
0answers
62views
Discretization of one-dimensional inhomogeneus Schröedinger equation
I was reading this article on numerical solutions for the non homogeneous schröedinger equation and when proposing a discretized solution it states: if we consider the time-dependent schröedinger ...
3votes
0answers
89views
Large-scale rotational invariance in lattice space
It is often claimed among physicists that rotational invariance can emerge at large scales in lattice space. Let's focus on quantum mechanics for now. I interpret this claim as follows (I am a ...
- 31
5votes
3answers
3kviews
On using Python to solve Time Independent Schrodinger Equation, the eigenfunctions have their values "pushed" to one of the boundaries?
I am having trouble using numerical methods to solve Time Independent Schrodinger Equation. I am considering a quartic potential function: $$ V(x) = x^4 -4x^2.$$ $$ -\frac{d^2\psi(x)}{dx^2} + V(x) \...
3votes
0answers
133views
Continuum solutions for the Dirac equation in Coulomb potential - numerical codes
Following the representation used in [1, pag. 11] the solution of the Dirac equation in polar coordinates for energy $E$ is of the type: $$ \psi_{E\kappa m}(\bf{r})= \dfrac{1}{r} \Bigg( \begin{matrix} ...
- 81
0votes
1answer
73views
Normalization of a wavefuntion [closed]
I am working with the following wavefuntion which describes two entangled photons. I need to normalize it over the frequency domain, $\omega_\alpha$ and $\omega_\beta$ are the frequency of the ...
- 39
1vote
1answer
117views
Restrictions on Initial Values for the first derivatives of a wavefunction, for a bound state in the time independent Schrödinger Equation?
The time independent wave function for a bound state given some potential function $V(r)$ is given by the time independent Schrödinger Equation $$E\Psi=-\frac{\hbar^2}{2m}\left(\frac{\partial^2\Psi}{\...
- 2,031
-1votes
1answer
596views
Transmission coefficient of a Gaussian wave packet through a potential barrier
I have simulated the scattering of a gaussian wave packet with a potential barrier (Crank-Nicolson), and through many simulations I have determined the dependence of the transmission coefficient with ...
0votes
0answers
115views
How to choose boundary conditions for numerical solution of Schrodinger's equation whose solutions are expected to die out "at infinity"?
I am using the "Shooting method" for solving the TISE with a "reasonably arbitrary" potential in 1D,with boundary conditions such that the eigenfunctions $\psi_n\to0$ as $x\to\infty$(And another ...
- 1,108
2votes
2answers
88views
Number of nodes in Hartree-Fock solution
The Hartree-Fock equation for atoms is of the form $\left[\frac{d}{dr^2}+f(r)-\epsilon\right]P(r)=g(r) \tag1$ Usually algorithms to solve this equation assumes that the number of nodes of $P(r)$, ...
1vote
0answers
224views
Double zeta polarised, triple zeta double polarized. What is the definition?
I understand that a single zeta basis contains the hydrogen stationary states $\psi_{nlm_l}$ for a particular selection of quantum numbers $(n,l,m_l)$. You can decide the quantum numbers that will be ...
- 1,460
-1votes
1answer
216views
Why are numerical solutions for the Schrödinger equation necessary to plot this free waves solution?
Suppose a particle in free space given by: $$\psi(x,t) = Ae^{ik(x-\frac{\hbar k}{2m}t)} + Be^{-ik(x-\frac{\hbar k}{2m}t)}.$$ Why are numerical solutions necessary in order to plot this? Why can't ...
