# Approximate Quantum Mechanical Methods

- Page ID
- 127063

- 420: A Rudimentary Model for Alpha Particle Decay
- Simple models for the potential energy experienced by an alpha particle in a nucleus have the form shown below. In the interest of mathematical simplicity we will not attempt to model any particular alpha emitter, but just try to capture the essentials of the quantum mechanical tunneling mechanism for alpha decay that was formulated by Gamov, Gurney and Condon in 1928.

- 433: Variation Method for the Harmonic Oscillator
- This exercise deals with a variational treatment for the ground state of the simple harmonic oscillator which is, of course, an exactly soluble quantum mechanical problem.

- 436: Gaussian Trial Wavefunction for the Hydrogen Atom
- A Gaussian function is proposed as a trial wavefunction in a variational calculation on the hydrogen atom.

- 452: Variational Calculation for the Polarizability of the Hydrogen Atom
- In this exercise the polarizability of the hydrogen atom is calculated.

- 453: Hybrid Variational Calculation for the 1D Hydrogen Atom with Delta Function Potential
- This hybrid variational calculation on a one‐dimensional model of the hydrogen atom using a delta function potential interaction between the proton and electron yields the correct ground state energy. The model is composed of two peculiar elements: a trial wave function that has discontinuity at x = 0 and a potential energy interaction that is zero everywhere except at x = 0.