Week 10 Uncertainty Principle & Schrodinger Equation

Question 1

what is the Uncertainty principle equation

Answer 1

ΔxΔp = αh(bar) / 2

Question 2

when is the uncertainty principle used

Answer 2

when α is unknown

Question 3

what is the energy-time uncertainty relation equation

Answer 3

αh(bar) / 2 = ΔEΔt

Question 4

what is the procedure to find frequency of a photon using the energy time uncertainty

Answer 4

1 say Δt is very large so that the photon could be anywhere so we can find p
2 use the momentum to find E
3 recall that E = hf so hΔfΔt ~ h(bar) => ΔfΔt ~ 1

Question 5

what can the Schrodinger equation be used for

Answer 5

it can be used to derive Ψ

Question 6

what does the time independent Schrodinger equation refer to

Answer 6

the Schrodinger equation that works/corresponds to particles of definite energy

Question 7

what is the Hamiltonian of a system and its accompanying equation

Answer 7

Total energy of a system
H = p^2 / 2m + V
V is the potential energy

Question 8

what is the time independent Schrodinger equation

Answer 8

EΨ(x) = ( -h(bar)^2 / 2m d^2/dx^2 + V(x) ) Ψ(x)

Question 9

How do V and Ψ relate to each other

Answer 9

If V is infinite then Ψ must be 0

If V is 0 then Ψ can be found

Question 10

why is energy quantised

Answer 10

because λ is quantised due to the general equation

λ = 2L/n , where n is the energy level