All Questions
Tagged with computational-physics wavefunction
39 questions
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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3
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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 ...
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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: $$ V(x) = x^4 -4x^2.$$
$$
-\frac{d^2\psi(x)}{dx^2} + V(x) \...
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Continuum solutions for the Dirac equation in Coulomb potential - numerical codes
Following the representation used in [1, pag. 11] the solution of the Dirac equation in polar coordinates for energy $E$ is of the type:
$$ \psi_{E\kappa m}(\bf{r})= \dfrac{1}{r} \Bigg( \begin{matrix}
...
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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 ...
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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
$$E\Psi=-\frac{\hbar^2}{2m}\left(\frac{\partial^2\Psi}{\...
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Transmission coefficient of a Gaussian wave packet through a potential barrier
I have simulated the scattering of a gaussian wave packet with a potential barrier (Crank-Nicolson), and through many simulations I have determined the dependence of the transmission coefficient with ...
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How to choose boundary conditions for numerical solution of Schrodinger's equation whose solutions are expected to die out "at infinity"?
I am using the "Shooting method" for solving the TISE with a "reasonably arbitrary" potential in 1D,with boundary conditions such that the eigenfunctions $\psi_n\to0$ as $x\to\infty$(And another ...
- 1,108
2
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2
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Number of nodes in Hartree-Fock solution
The Hartree-Fock equation for atoms is of the form
$\left[\frac{d}{dr^2}+f(r)-\epsilon\right]P(r)=g(r) \tag1$
Usually algorithms to solve this equation assumes that the number of nodes of $P(r)$, ...
- 525
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Double zeta polarised, triple zeta double polarized. What is the definition?
I understand that a single zeta basis contains the hydrogen stationary states $\psi_{nlm_l}$ for a particular selection of quantum numbers $(n,l,m_l)$. You can decide the quantum numbers that will be ...
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Why are numerical solutions for the Schrödinger equation necessary to plot this free waves solution?
Suppose a particle in free space given by:
$$\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 ...
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