topic 3

Question 1

ψ^2 (wavenumber squared)

Answer 1

• at any given point in space gives the probability of finding the particle at that point (born interpretation)

Question 2

wavefunction

Answer 2

• represents the spatial distribution of a particle

Question 3

probabilites must be

Answer 3

postive and real
- use modulus

Question 4

modulus of wavefunction squares

Answer 4

gives the probability density

Question 5

a wavefunction is said to be normalized if

Answer 5

• sun of modulus wavenumber squared at all points in space = 1
• mathematical equivalent of integration

Question 6

quantiziation of wavefunction rules

Answer 6

• must be contiuous
• gradient must be constinuous
• must have single value at any point in space
• must be finite
• cannot be zero everywhere

Question 7

heisenberg uncertainity principle

Answer 7

• uncertainity in position x uncertainity in momentum is greater than or equal to reduced planks constant over 2
• i.e there is no concept of particle trajectory
• can know both momentum and postion if in different axis

Question 8

to localise a wavefunction in space must (specifiy posititon)

Answer 8

• wave of different wavelenghts must be superimposed to form large change in momentum (p=h/wavelength)

Question 9

zero point energy

Answer 9

• vibration energy doesn’t eqaul zero even at T=0K
• also consequence of uncertainity principle

Question 10

equation relating energy and lifetime

Answer 10

• change energy x change in lifetime greater than or equal to reduced planks constant
• leads to lifetime broadening of spectral lines
• short lived excited states possess large uncertainty in the energy of the state
• leads to broad peaks in spectrum

Question 11

eigenfunction equation

Answer 11

operator x wavefunction = observable propertity (eigenvalue) x wavefunction

Question 12

operators

Answer 12

• instructions to carry out an action on wavefunction
• if it gives back the same function multiped by a constant it is referered to as eigenfunction
• and constant in output is eigenvalue

Question 13

operator for position in the X - direction

Answer 13

• multipication by x

Question 14

operator for linear momentum in the x -direction

Answer 14

• check book

Question 15

commutation

Answer 15

• the operators do not communicate in quantum mechanics therefore order operations are done is important
• operation1 x opertaion 2 - operation 2 x operation 1 do not equal 0

Question 16

expectation values of operator

Answer 16

• calculates mean value of a large number of measurement of an observable
• if wavefucntion normilaised doniminator = 1
• if wavefunction is an eigenfunction of operator A, the exception value is actually the same as the eigenvalue