Variational Iterative Time Dependent Method for Eigenvalues and Eigenfunctions of the Hamiltonian.

Area of Science:

• Quantum Mechanics
• Computational Chemistry
• Theoretical Physics

Background:

• Accurate determination of eigenvalues and eigenfunctions is crucial in quantum mechanics.
• Traditional methods can be computationally intensive, requiring extensive time evolution data.

Purpose of the Study:

• To develop a computationally efficient method for determining eigenvalues and eigenfunctions.
• To reduce the required time interval for accurate quantum mechanical calculations.

Main Methods:

• Combines short-time wave packet evolution with the variational theorem.
• Utilizes a correlation function and its time derivative as input, similar to the Filter Diagonalization Method.
• Employs an iterative and convergent approach.

Main Results:

• The method achieves convergence with short time intervals, significantly shorter than Fourier times.
• Successfully applied to model problems, including calculating tunneling splitting energies.
• Determined the ground tunneling state in a quartic double well potential using semiclassical initial value representation.

Conclusions:

• This method offers a computationally efficient alternative for quantum mechanical calculations.
• It demonstrates the possibility of obtaining tunneling phenomena using only classical paths.
• Has potential implications for ab initio computation of molecular electronic energies.