1-d Schrodinger Equation Eigenstates

by Cemal Yalabik, Bilkent University, Physics Department.

The red graph at the bottom of the window below corresponds to the potential energy of a one dimensional square potential well. On the top, the eigenfunction corresponding to the ground state of the quantum well should appear. A horizontal line on the potential plot indicates the energy eigenvalue level. The boundaries at the window edges are assumed to be at infinitely high potential.

You can move the mouse to the potential area and change the potential by pushing the left mouse button down and plotting in your modification. As soon as you release the button, the eigenfunction will start changing, converging to its new form. The ground state is found by repeated multiplication with the inverse of the Hamiltonian. The excited states are determined similarly, projecting out the lower energy states before each multiplication. One can therefore watch first the convergence of the ground state eigenfunction, then the development of the higher excited states, if selected.

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July 1997 Cemal Yalabik at