2019 May | Quantum Science Philippines

## Archive for May, 2019

### Finding the commutator of the Hamiltonian operator, H and the position operator, x and finding the mean value of the momentum operator, p

Friday, May 24th, 2019

By Kim S. Ponce, MS Physics, MSU-IIT   Problem Given that the Hamiltonian is . Show that and the mean value of the momentum () is zero. Solution Substituting our Hamiltonian operator,     Using the commutator of and , this can be written in the form:     But , so     Therefore, […]

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### Angular momentum: Show that [L^2,Lz] = 0

Friday, May 24th, 2019

Show that Solution: Let  act on eigenfunction that is,   Where we recall that Thus we have,   Since the eigenfunction is arbitrary, we can conclude that

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### The Ionization energy, radius and velocity of a Hydrogen atom

Friday, May 24th, 2019

a. Show that The Ionization energy is the energy needed to remove the electron from an atom. The formula for the Ionization energy of a hydrogen atom in ground state is given by,   First we must obtain the values of and . is the reduced mass with the formula: where, (mass of the electron) […]

### Derivation of the Energy of the Bohr model of a hydrogen atom

Friday, May 24th, 2019

Problem: Derive   Solution We start with the three equations below,       Equation 1 is an expression of the fact that the total energy E of an electron is the sum of its kinetic energy and its potential energy . Equation 2 is the fundamental equation of Newtonian dynamics, is the Coulomb force […]

### The Lagrangian and the Classical Hamiltonian of a two-particle system

Thursday, May 23rd, 2019

Vanessa V. Destura, MSU-IIT Figure 1. A two-particle system We consider two particles in a system, that is, and . The relative coordinate , is given by We replace the positions and by the center of gravity, Now, using equations and to solve for the expressions of and , we have So,   In Classical […]

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