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Feb
1
comment How to numerically solve a 1-d time-independent Schrodinger equation?
The closer to the "ionization threshold" you get, the larger the true wave functions are. I don't think any simple boundary condition can fix the resulting errors, unless the domain is made larger (which eventually makes NDEigensystem run out of time or memory). Arnoldi is (I believe) the default method, I just added it explicitly so that I can also try out different sub-methods (such as `"Shift"). With or without shift, you should of course get the same eigenvalues, but sorted differently. But different sorting (default is absolute value) means the ground state comes much later in the list.
Feb
1
comment How to numerically solve a 1-d time-independent Schrodinger equation?
I was initially confused about your use of Neumann boundary conditions. I think you must mean something else, because by comparing with your desired eigenvalues I concluded that you're really solving the radial equation for the reduced wave function, where no Neumann boundary condition is needed. The biggest problem is how to deal with the conditions of vanishing amplitude at infinity.
Feb
1
revised How to numerically solve a 1-d time-independent Schrodinger equation?
address shift option and boundary conditions
Feb
1
revised How to numerically solve a 1-d time-independent Schrodinger equation?
address shift option
Feb
1
revised How to numerically solve a 1-d time-independent Schrodinger equation?
copy-paste error corrected
Feb
1
revised How to numerically solve a 1-d time-independent Schrodinger equation?
formatting of table
Feb
1
comment Incorrect Left and Right Eigenvectors in Mathematica
Contrary to what you're claiming, the eigenvalues you're comparing are not the same, so there is no contradiction.
Feb
1
revised How to numerically solve a 1-d time-independent Schrodinger equation?
typo
Jan
31
awarded  Enlightened
Jan
31
answered How to numerically solve a 1-d time-independent Schrodinger equation?
Jan
31
comment How to numerically solve a 1-d time-independent Schrodinger equation?
Your code doesn't run because Alpha is undefined. Where did you get the values in the last table?
Jan
31
comment How to numerically solve a 1-d time-independent Schrodinger equation?
You might find this useful: Solving the Schroedinger equation for bound states with Mathematica 3.0 (arXiv link).
Jan
31
reviewed Approve How to numerically solve a 1-d time-independent Schrodinger equation?
Jan
31
awarded  Nice Answer
Jan
31
comment Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square
I added another paragraph on accidental degeneracies.
Jan
31
revised Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square
Added more explanation
Jan
31
comment Incorrect Left and Right Eigenvectors in Mathematica
Possibly related: Orthonormalization of non-hermitian matrix eigenvectors
Jan
31
revised Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square
Accidental degenracies
Jan
31
revised Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square
Accidental degenracies
Jan
31
revised Non Standard Eigenfunction Plots of the Laplacian Over the Unit Square
Completed the formal projector treatment.