A program for the calculation of energy eigenvalues and eigenstates of a schrödinger equation

✍ Scribed by V. Fack; G. Vanden Berghe

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 724 KB
• Volume: 39
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(86)90130-x

✦ Synopsis

Title of the program: SCHROD dimensional Schrodinger equation Catalogue number: AADV dy(x) +(E-V(x))y(x)=0, Program obtainable from: CPC Program Library, Queen's Uni-where E denotes the eigenvalue parameter and V(x) the potenversity of Belfast, N. Ireland (see application form in this issue) tial. Computer: Siemens 7000 Series; Installation: CDR, Rijksuni-Method of solution versiteit Gent, Krijgslaan 281-S9, B 9000 Gent, Belgium A finite difference representation for d 2y(x)/dx2 is introduced such that the Schrodinger equation is transformed into Operating system: BS2000 an algebraic eigenvalue problem. This problem can be reduced to the calculation of the ei'genvalues and eigenvectors of a Programming language: FORTRAN 77 symmetric tridiagonal matrix, to which the NAG [11 routine FO2BEF can be applied. High speed storage required: 240 673 words Restrictions on the complexity of the problem No. of bits in a word: 32 It is assumed that the wavefunctions are restricted to obey the Dinchlet boundary condition y(x) = 0 at some x-value R. Peripherals used: card reader or VDU, printer Typical running time No. of lines in combined program and test deck: 439

The running time depends on the choice of the value R, on the number of terms in the finite difference representation for Keywords: SchrOdinger equation, energy eigenvalues and eigen-d2y(x)/dx2 and on the considered steplength h. functions, finite difference approach, reduction of band width Reference Nature of physical problem

[1] Numerical Algorithms Group (NAG) Library Manual, Calculation of the energy eigenvalues and eigenstates of the one Mark 8 (1981).