An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes
A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional
axisymmetric region is developed. The boundary of the region
is defined by an arbitrary analytic function. The method uses a
coordinate transformation and an expansion in eigenfunctions. The
effectiveness is checked and confirmed by applying the method to a
particular example, which is a prolate spheroid.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50981", author = "İnci M. Erhan", title = "An Expansion Method for Schrödinger Equation of Quantum Billiards with Arbitrary Shapes", abstract = "A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional
axisymmetric region is developed. The boundary of the region
is defined by an arbitrary analytic function. The method uses a
coordinate transformation and an expansion in eigenfunctions. The
effectiveness is checked and confirmed by applying the method to a
particular example, which is a prolate spheroid.", keywords = "Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics", volume = "1", number = "5", pages = "234-4", }