Partial differential equation which describes the time evolution of the wavefunction of a quantum system. It is one of the first and most fundamental equations of quantum mechanics.
5
votes
2answers
2k views
Solving one dimensional Schrodinger equation with finite difference method
Consider the one-dimensional Schrodinger equation
$$-\frac{1}{2}D^2 \psi(x)+V(x)\psi(x)=E\psi(x)$$
where $D^2=\dfrac{d^2}{dx^2},V(x)=-\dfrac{1}{|x|}$.
I want to calculate the ground state ...
10
votes
2answers
683 views
Schrodinger equation in spherical coordinates
I read a paper on solving Schrodinger equation with central potential, and I wonder how the author get the equation(2) below. Full text.
In Griffiths's book, it reads
...
4
votes
2answers
673 views
On numerically solving the Schrödinger equation
I just read a paper 'A pocket calculator determination of energy eigenvalues' by J Killingbeck
(1979).
Link: http://iopscience.iop.org/0305-4470/10/6/001
I have some questions about section 2.
Why ...
2
votes
1answer
2k views
How to solve this Schrödinger equation?
I am taking an intro level quantum mechanics class. Our textbook gives a problem like this:
The deuteron is a nucleus of "heavy hydrogen" consisting of one proton and one neutron. As a simple ...
1
vote
1answer
279 views
Is it possible that Atomic Electron Probability Density is a result of Heat?
The Schrödinger Equation provides a Probability Density map of the atom. In light of that, are either of the following possible:
The orbital/electron cloud converges to a 2d surface without heat ...
4
votes
2answers
2k views
Zero probability of finding an electron in the nucleus
One and the same electron in a p orbital and taking part in a common π (pi) bond has two lobes visualized as connecting through the nucleus. There is however zero probability of finding an electron at ...
8
votes
5answers
828 views
The Many Body problem
(This is a simple question, with likely a rather involved answer.)
What are the primary obstacles to solve the many-body problem in quantum mechanics?
Specifically, if we have a Hamiltonian for a ...
