Week 9 Infinite Square Well & Momentum

Question 1

describe the infinite square well scenario

Answer 1

a particle is restricted to a region between 0 and L and only travels in one direction

Question 2

what can be observed of a particle with definite energy in this square well

Answer 2

it’s Ψ is confined to exact discrete values

Question 3

what is the normalisation for Ψ when restricted to a region of length L

Answer 3

Ψ(n) = Asin(nπx/L)

A is some complex number

Question 4

what does the wave function tell us about a particle for quantum physics

Answer 4

everything we need to know allowing us to calculate all properties of the particle

Question 5

what are the two p related equations that involved interchanging h with ħ

Answer 5

p = ħk
p = h/λ

Question 6

define the differential operator for momentum

Answer 6

p(hat) = -ih(bar) d/dx

Question 7

what is the equation relating p and p(hat)

Answer 7

pΨ = p(hat)Ψ

Question 8

what is the uncertainty is momentum equation

Answer 8

Δp = sqrt[ <p> - </p><p>^2 ]</p>

Question 9

what is the Heisenberg Uncertainty principle equation and what is the important condition

Answer 9

ΔxΔp = αh(bar) / 2

α >= 1

Question 10

what does the uncertainty principle essentially state

Answer 10

As Δx tends to infinity Δp tends to 0 in order to combat this and the reverse is true. Therefore it is impossible to know both the position and momentum of a particle to arbitrary accuracy