# Numerical Solutions for Schrödinger's Equation

- Page ID
- 127067

Numerically solving the Schrödinger equation is a complex problem that stems from the large number of points needed on a grid and the requirement to satisfy boundary conditions.

- 395: Introduction to Numerical Solutions of Schödinger's Equation
- Solving Schrodinger's equation is the primary task of chemists in the field of quantum chemistry. However, exact solutions for Schrödinger's equation are available only for a small number of simple systems. Therefore the purpose of this tutorial is to illustrate one of the computational methods used to obtain approximate solutions.

- 401: Particle in a Slanted Well Potential
- Numerical Solutions for Schrödinger's Equation for the Particle in the Slanted Box.

- 402: Numerical Solutions for a Particle in a V-Shaped Potential Well
- Schrödinger's equation is integrated numerically for a particle in a V-shaped potential well.

- 404: Numerical Solutions for a Double-Minimum Potential Well
- Schrödinger's equation is integrated numerically for a double minimum potential well: V = bx⁴ - cx².

- 405: Numerical Solutions for the Quartic Oscillator
- Schrödinger's equation is integrated numerically for the first three energy states for the quartic oscillator.

- 406: Numerical Solutions for Morse Oscillator
- Schrödinger's equation is integrated numerically for the first three energy states for the Morse oscillator.

- 407: Numerical Solutions for the Lennard-Jones Potential
- Merrill (Am. J. Phys. 1972, 40, 138) showed that a Lennard-Jones 6-12 potential with these parameters had three bound states. This is verified by numerical integration of Schrödinger's equation.

- 410: Another Look at the in a Box with an Internal Barrier
- The purpose of this tutorial is to explore the impact of the presence of a large (100 Eh) thin (0.10 a0) internal barrier on the solutions to the particle-in-a-box (PIB) problem. Schrodinger's equation is integrated numerically for the first five energy states.