Lecture 1 Flashcards
1.1. What we need from a theory of mechanics for quantum particles 1.2. The wave equation in quantum mechanics 1.3. The time-dependent Schrödinger Equation
What do you need to understand the ‘Mechanics’ of a particle?
- A description of the STATE
- An equation to describe the EVOLUTION with respect to time
In CLASSSICAL mechanics, what describes the state and evolution of a particle?
The position and momentum coordinates describe the state and Newtons second law describes the evolution.
In QUANTUM mechanics, what describes the state and evolution of a particle?
The wave function describes the state and the wave equation describes the evolution.
What is the wave equation for light?
Second partial derivative of A with respect to x = 1/c^2 second partial derivative of A with respect to t
What is the de broglie relation?
Lambda = h/p
What is the wavenumber (k)?
2 pi / lambda
What is a dispersion relation?
An equation which relates the wavelength or wavenumber of a wave to its frequency.
What is the one-dimensional time-independant Shrodinger equation? [red]
ihbarpartial psi/ partial t = -hbar^2/2m *2nd partial psi/second partial x + V psi
What is the 5th postulate of Quantum Mechanics? [red]
“The development of the wavefunction with respect to time is governed by the TISE.”
What is the dispersion relation for non-relativistic particles with mass?
E = p^2/2m +V
