FDSC 230 Lecture Notes - Lecture 4: Boundary Value Problem, Reduced Mass, Diatomic Molecule

• School: McGill University
• Department: Food Science
• Course: FDSC 230
• Professor: Varoujan Yaylayan

Document Summary

We need to find the stationaty states of quantum mechanical harmonic oscillator. The mass is changed for the reduced one ( ) and the potential energy is replaced for the. Hookean potential, given rise to this equation. x. The solution to this differential equation is the infinite sum of wavefunctions. x n n x n x. If we based ourselves on only this equation, we see that no quantization number appears here because the function gives a continuous set of solutions, which are not the solutions for the quantum mechanical system of the harmonic oscillator. To get them, we need to apply boundaries conditions. As x infinite , the potential energy v infinite, so the wavefunction zero. The probability of finding the particle must decrease towards zero as the distance from the orgin increases towards infinity. Which means that it is less likely to find the particle at very far distances from the origin.