Week 8 Intro to Quantum Physics & The Wave Function

Question 1

what did Young determine was a property of light and how

Answer 1

light is a wave

double slit experiment

Question 2

what do we now know about Young’s double slit experiment for light

Answer 2

although light does produce the light and dark regions that would be expected by a wave these regions are built up dot by dot from the light particle (photon)

Question 3

what does the double slit experiment allow us to say about the position of individual particles

Answer 3

we can’t predict where a single particle will end up only the probability that we will find it there.

Question 4

what is the de Broglie wavelength equation and why is it important

Answer 4

h = λp

it is important because it is true for all particles

Question 5

what does the wave function tell us and what denotes it

Answer 5

the likelihood of a particle being at a point. It is denoted by Ψ

Question 6

what must be done to Ψ in order for it to be made useful

Answer 6

we make Ψ the modulus of a complex number

Question 7

what is the general exponential equation for Ψ and its trigonometric counterpart

Answer 7

Ψ ∝ e^ikx = cos(kx) + isin(kx)

k is the wavenumber = 2pi/λ

Question 8

what is true of modulus Ψ

Answer 8

I Ψ I is constant

Question 9

what does Born’s rule tell us for IΨI^2 in equation terms

Answer 9

IΨI^2 = Ψ*Ψ = prob dist

Question 10

what do we do to Ψ to find the probability of finding it and how is this done

Answer 10

we normalise it

this is achieved by making the integral of IΨI^2 with limits infinity and negative infinity = to 1

Question 11

what is the equation for finding < x^n >

Answer 11

< x^n > = ∫ x^n IΨI^2 dx

with limits @ pos and neg infinity

Question 12

what is the uncertainty in position equation

Answer 12

σ = sqrt[ - ^2 ]