We introduce an additional method to solve Schrödinger’s equation for a free particle in an infinite well of arbitrary shape ~the Helmholtz equation with Dirichlet boundary conditions!, a problem of interest in the area of quantum chaos. We expand the wave function in a basis of products of sine functions, then use the constraint operator to contain the wave function to a region within the doma...

The method of undetermined coefficients is commonly applied to solve linear, constant coefficient, non-homogeneous ordinary differential equations when the forcing function from a selected class functions. Often hyperbolic sine and cosine functions are not explicitly included in this list Through set guided examples, work argues that ought be select Careful explanation provided for necessary tr...