210
16 Hermite Polynomials
(optional, default “yes”) has the value “no” no wave function will be plotted, and
“s” (optional) is the coordinate vector for visualizing the wave functions with
default 2000 equidistant values between −5 · · · 5. The output arguments are “E” the
energy eigenvalues, “V” the corresponding eigenvector and “testwave” the relative
smallest contribution to each eigenvector. This should be a small number. A typical
example is
>> kappa = 0.2; lambda = 1; hmany = 5; ndim = 35;
[E,V, tw] = anharmosc(kappa, lambda, hmany, ndim);
The graphical user interface >> anha01 uncovers the changes of the first two
eigenfunctions in dependence of λ, κ and should be self-explanatory.
References
1. Cohen-Tannoudji, C., Diu, B., Laloe, F.: Quantum Mechanics. Hermann, Paris (1977)
2. Gradstein, I.S., Rhysik, I.M.: Tafeln · Tables II. Verlag Harry Deutsch Thun, Frankfurt A. M.
(1981)
3. Hillery, M., O’Connell, R.F., Scully, M.O., Wigner, E.P.: Distribution functions in physics:
fundamentals. Phys. Rep. 106, 121 (1984)
4. Ho, Y.K.: The method of complex coordinate rotation and its application to atomic collision
processes. Phys. Rep. 99, 1 (1983)
5. Nikiforov, A.F., Suslov, S.K., Uvarov, V.B.: Classical Orthogonal Polynomials of a Discrete
Variable. Springer, Berlin (1991)
6. Schweizer, W.: Numerical Quantum Dynamics. Kluwer Academic Publishers, Dordrecht (2001)
16 Hermite Polynomials
(optional, default “yes”) has the value “no” no wave function will be plotted, and
“s” (optional) is the coordinate vector for visualizing the wave functions with
default 2000 equidistant values between −5 · · · 5. The output arguments are “E” the
energy eigenvalues, “V” the corresponding eigenvector and “testwave” the relative
smallest contribution to each eigenvector. This should be a small number. A typical
example is
>> kappa = 0.2; lambda = 1; hmany = 5; ndim = 35;
[E,V, tw] = anharmosc(kappa, lambda, hmany, ndim);
The graphical user interface >> anha01 uncovers the changes of the first two
eigenfunctions in dependence of λ, κ and should be self-explanatory.
References
1. Cohen-Tannoudji, C., Diu, B., Laloe, F.: Quantum Mechanics. Hermann, Paris (1977)
2. Gradstein, I.S., Rhysik, I.M.: Tafeln · Tables II. Verlag Harry Deutsch Thun, Frankfurt A. M.
(1981)
3. Hillery, M., O’Connell, R.F., Scully, M.O., Wigner, E.P.: Distribution functions in physics:
fundamentals. Phys. Rep. 106, 121 (1984)
4. Ho, Y.K.: The method of complex coordinate rotation and its application to atomic collision
processes. Phys. Rep. 99, 1 (1983)
5. Nikiforov, A.F., Suslov, S.K., Uvarov, V.B.: Classical Orthogonal Polynomials of a Discrete
Variable. Springer, Berlin (1991)
6. Schweizer, W.: Numerical Quantum Dynamics. Kluwer Academic Publishers, Dordrecht (2001)