Applications of the fourier transform path integral method

Sutisna Sutisna

The path integral is a method that often used in the quantum problems calculation. For example; the calculation of quantum system energy that has complex potential form. The method gives more easily than perturbation method. The method is also used to derive Green function, which usually used Fourier transformation. The Green function has widely application in quantum physics, since it used to compute solution of inhomogen differential equation as Schrodinger equation. In the particle physics, the Green function used as propagator in Feynman’s diagram. Considering the importance of Green function, and the powerfull of path integral method, in the paper, the method used to derive the formula of Green function for quantum harmonic oscillator system. The system has widely application to give more information of physical phenomena, for example, the atomic vibration in solid state. The result was also compared with Fourier transformation method and both give the same result as hoped.

Eugene P. Gross

Maurice M. Mizrahi

The author investigates the new approach to path integrals in quantum mechanics recently introduced by C. DeWitt-Morette, which has the advantage of not resting on the usual limiting process. It defines the suitable measures on the infinite-dimensional function spaces by their Fourier transforms, which are simple, closed-form expressions.

Osvaldo Civitarese, Manuel Gadella

Tommi Höynälänmaa

We present a method for the path integral formulation of electronic structure simulation. The time evolution operator is represented as matrix in a basis consisting of Deslauriers-Dubuc or Daubechies wavelets. We present an approximation of the path integral kernel and a method for calculating wavefunctions. The kernel is tested by finding wavefunctions and eigenenergies of one-dimensional and three-dimensional harmonic oscillators and hydrogen atom in one and three dimensions.