Quantum Mechanics (Module 1)

ch 5

Quantum Mechanics

Study of the motion of sub-atomic particles

matter waves (phenomenon)

aka de broglie waves
particles when moving exhibit wave like properties

Energy equations

energy of light wave and light particle

relation of wave nature and particle nature

Planck’s constant

6.626×10^-34 m²kg/s

accelerate particles

To accelerate a particle an external potential is applied. The applied external potential is proportional/related to the energy of the particle.

Heisenberg’s Uncertainity Principle

It is impossible to find the position and momentum of a particle simultaneously.

Canonically conjugate variables

position and momentum
angular displacement and angular momentum

energy and time

radius of the nucleus

10^-14 m

applications of uncertainity principle

1. Absence of e- in the nucleus

2. Uncertainity of frequency of light emitted by the atom

3. Natural line broadening

Absence of electrons in the nucleus

Uncertainity of the frequency of the light emitted by the atom

Natural Line broadening

Probability of finding the particle in unit volume

Probability density of a volume

Normalization condition

If a particle is definitely present within the probablity density it can be equated to 1.

general wave representation

wave function of wave propagating with momentum p (derive) in the x-direction

Schrodinger’s Equation (derive) Time dependent

Schrodinger’s Equation (derive) Time Independent

Particle in a Box