Chem 5021

quantum mechanics

Wavelengths of coloured light

Violet: 380 to 450 nm

Blue: 450 to 495 nm

Green: 495 to 570 nm

Yellow: 570 to 590 nm

Orange: 590 to 620 nm

Red: 620 to 750 nm

Wavenumber

K = 2π/λ

de Broglie wavelength formula

Wave Velocity

Angular wave number

Angular frequency

Einstein wave equation

Einstein special relativity equation

The de Broglie relationship

Reduced planks constant

Classical kinetic energy of electron

Schrodinger equation

Electron density

Free electron wavefunction

Heisenberg uncertainty principal

Particle In a box wavefunctions (unnormalized)

Derivatives

Integrals

Particle in a box wavenumber

Particle in a box energy

PIB model energy difference

Particle in a box probability densities

Normalised PIB states

Overlap integral

How to find out if states are orthogonal?

If the product of two states has odd parity we know (without doing the maths) that the states are orthogonal

For states with the same parity, we’d need to evaluate the overlap integral.

Particle on a ring

one-dimensional model

The boundary conditions are that the wavefunction is single valued and continuous

simple model of aromatic molecules in which the pi-electrons are delocalised around the ring

How are position and angle related

Evaluate kinetic energy operator in terms of angle

Normalised POR wavefunction

POR energy