Exam flashcards

Question 1

What is the rule for a transitition?

Answer 1

Δl = ±1
Δm = 0,±1

Question 2

What is the emission spectrum for a de-excitation?

Answer 2

A single sharp peak

Question 3

What is the energy separation for a magnetic field?

Answer 3

μ_BB/e

Question 4

What is spin orbit coupling?

Answer 4

Electron with l>0,feel magnetic field due to charged nucleus in its rest frame
Field interacts with spin magnetic moment, lifting spin degeneracy of states

Question 5

What is screening?

Answer 5

Shielding of nuclear charge by negative electron charge
Shell structure has higher n states closer to nucleus
Outer shell electrons experience less positive charge

Question 6

What is the equation for expected energy in a well?

Answer 6

< E > = u₁p₁+u₂p₂+u₃p₃
Where p is the prefactor squared
u is an energy

Question 7

How do we find the density of states?

Answer 7

n(E) = dN/dE

Question 8

What is the makeup of a neutron?

Answer 8

n = udd

Question 9

What is the makeup of a proton?

Answer 9

p = uud

Question 10

What is the boson for the beta minus decay and its properties?

Answer 10

W^-
Spin = 1
Mass = 80m_p

Question 11

What is a harmonic potential for a diatomic molecule?

Answer 11

Two atoms with a chemical bond
x represents deviation from equilibrium
k’ represents “stiffness” of the chemical bond.
𝜔 is the oscillation rate of the equivalent classical mass-and spring system. 𝜔 = √𝑘′/𝜇
The reduced mass is 𝜇 =𝑚1𝑚2/(𝑚1+𝑚2)

Question 12

What is the sum of even functions?

Answer 12

An even function

Question 13

Why is the SHO an even function?

Answer 13

U(x) is even
The SHO is a sum of U(x)

Question 14

What is the wave function for a time t>T?

Answer 14

Collapse to a state of u(x)

Question 15

Is the energy of a system equal for 0 < t < T equal to < E >

Answer 15

No
The energy was indeterminate before
The expectation value gives an “average” and is not
applicable to a single quantum system.

Question 16

What is a well behaved function?

Answer 16

Goes to 0 as x goes to infinity

Question 17

What is the eigenvalue for a Hermitian operator?

Answer 17

Real

Question 18

How do valence electrons relate to density?

Answer 18

More valence electrons per atom given an increased density

Question 19

How do we estimate an appropriate Z value?

Answer 19

Charge on nucleus minus 0.3 for screening effects

Question 20

What is the difference between an insulator and a metal?

Answer 20

Metal: E_F lies within a band with states above. Material can conduct
Insulator: E_F lies outside of a band with no states near. Material cannot conduct

Question 21

How did Dirac predict anti particles?

Answer 21

Dirac proposed the existence of negative energy states;
These are all occupied
Pauli Exclusion Principle prevents the positive energy particles falling into these filled states.
Dirac equation has solutions by the relativistic Energy-Momentum relation

Question 22

What is |1>?

Answer 22

|1> = a|↑>+b|↓>

Question 23

What is |2>?

Answer 23

|2> = a|↑>-b|↓>

Question 24

What is the magnitude of the orbital angular momentum in the x-y plane?

Answer 24

sqrt(L²-L_z²)

Question 25

What is the expectation value of the potential energy?

Answer 25

1/2 of the ground state energy

Question 26

What is the equation for ψ(0)?

Answer 26

ψ(0) = c₁ψ₁+c₂ψ₂ etc

Question 27

What is the normalisation factor?

Answer 27

(c₁²+c₂²)^-1 etc

Question 28

What are the probabilities?

Answer 28

c₁² * normalisation factor c₂² * normalisation factor etc

Question 29

How do we maximise binding energy?

Answer 29

dE_B/dZ

Question 30

What are the differences between a classic and quantum oscillator?

Answer 30

Quantum has discrete energy levels Quantum has non-zero probability to to have a displacement beyond classical limit

Question 31

What is the representation of a dynamical variable?

Answer 31

Represented by Hermitian operators The eigenvalues represent measurements of a given quantity The relationship between operators of different quantities is the same as in classical physics

Question 32

What is the expectation value?

Answer 32

∫Y*LYdx Where L is an operator

Question 33

What is the change in energy for the strong Zeeman regime?

Answer 33

ΔE = - μ_BBΔM

Question 34

What are the energy levels for the strong Zeeman regime?

Answer 34

(2l+1)(2s+1)

Question 35

What is the Hamiltonian for the strong Zeeman regime?

Answer 35

-μ_B(m_l+2m_s)

Question 36

What is the expectation value of a matrix for a vector (a b)?

Answer 36

(i j) (a b) (i (c d) j)

Question 37

What is Hund’s first rule?

Answer 37

Electrons in a sub-shell align spins where possible to antisymmetrise spatial wave function and reduce Coulomb repulsion

Question 38

What is the equation for valence electron density?

Answer 38

nρ/m Where n is the number of valence electrons ρ is the mass density m is the atom mass