The effect of discontinuous wave functions on optimizations of VMC calculations of quantum systems

Here, a relatively good comparison has been done between the performance results of discontinuous and continuous forms of wave function on quantum systems as well. In this project, we’ve estimated the energy of ground and first state as the expectation value of Hamiltonian of harmonic oscillator and binding energy of nucleons confined in a Yukawa potential by making use of following three wave function: exponential, linear and Gaussian form which are convenient to optimize and may be evaluated rapidly are devised and tested and we stress the advantages of using expressions which are Gaussian in the variable parameters. Exponential function is quite different from a Gaussian ones as it has a cusp at x=0, hence a discontinuity in its derivatives. We then have performed to test inaccuracy of the discontinuous wave function and energy’s error of its exact value because using of exponential and linear function by mathematical statements of calculation of delta and Heaviside function and either VMC calculation of wave function optimization, as both of them will have the same result of error value. The result of our study is very promising for future applications of quantum Monte Carlo methods especially in many body systems.