The annihilation-creation operators a(±) are defined as the positive/negative frequency parts of the exact Heisenberg operator solution for the ‘sinusoidal coordinate’. Thus a(±) are hermitian conjugate to each other and the relative weights of various terms in them are solely determined by the energy spectrum. This unified method applies to most of the solvable quantum mechanics of single degr...

We discuss hybrid quantum-mechanics/molecular-mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) generalizations to our recently developed quantum wavepacket ab initio molecular dynamics methodology for simultaneous dynamics of electrons and nuclei. The approach is a synergy between a quantum wavepacket dynamics, ab initio molecular dynamics, and the ONIOM scheme. We utilize this...

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schrödinger's equation, which is half of the defining equations of Bohmian mechanics. I try ...

An elementary introduction is given to the subject of Supersymmetry in Quantum Mechanics which can be understood and appreciated by any one who has taken a first course in quantum mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct new exactly solvable n Hamiltonians having n-1,n-2,...,0 bound states. The rel...

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schrödinger's equation, which is half of the defining equations of Bohmian mechanics. I try ...

We present the path integral formulation of quantum mechanics and demonstrate its equivalence to the Schrödinger picture. We apply the method to the free particle and quantum harmonic oscillator, investigate the Euclidean path integral, and discuss other applications.

A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the eigenvalues. In quantum field theory the method provides a consistent second order extension of the gaussian effective potential. Typeset using REVTEX