Week 2 Operators, Commutators & Computability

Question 1

what is the TISE

Answer 1

-ħ^2 / 2m ∂^2/∂x^2 + V(x) = iħ ∂/∂t

Question 2

define an operator

Answer 2

something that acts on a wavefunction to give another wavefunction

Question 3

what is the Hamiltonian operator

Answer 3

H^ = -ħ^2/2m + ∂^2/∂x^2 + V(x)

Question 4

what is true of the different energies a wavefunction can accompany

Answer 4

they are the stationary states and eigenfunctions of the Hamiltonian

Question 5

what is true of observables and their operators

Answer 5

for any observable A there is an operator A^ whose eigenvalues {an} give the only possible value for measurements of A

Question 6

what is the momentum operator

Answer 6

px^ = -iħ ∂/∂x

Question 7

what is the position operator

Answer 7

x^ = x

Question 8

what defines a Hermitian operator

Answer 8

the conjugate of the hermitian operator is equal to itself

Question 9

what is the variance equation

Answer 9

(ΔA)^2 = <a> - </a><a>^2</a>

Question 10

what is the generalised uncertainty principle

Answer 10

(ΔA)(ΔB) >= |i/2 |