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Staudt Physics GRE > Quantum Mechanics & Atomic Physics > Flashcards

Quantum Mechanics & Atomic Physics Flashcards

1
Q

Expectation value of an observable

A
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2
Q

Probability of finding a particle somewhere

A
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3
Q

Hermitian operator facts

A
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4
Q

position and momentum operators

A
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5
Q

Expansion coefficient

A
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6
Q

Expectation value in a superposition of states

A
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7
Q

Definition of inner product behavior under complex conjugation of a bracket

A
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8
Q

Applying an operator to a bracket

A
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9
Q

Inner product on a function space

A
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10
Q

Time dependent Schrödinger equation

A
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11
Q

Hamiltonian operator

A
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12
Q
A
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13
Q

Commutator of the position and momentum operators

A
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14
Q

Generalized uncertainty principle

A
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15
Q

Variance

A
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16
Q

Uncertainty of position and momentum

A
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17
Q

“Folklore” uncertainty of x and p

A

ΔxΔp ≈ ħ

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18
Q

“Folklore” uncertainty of energy and time

A

ΔEΔt ≈ ħ

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19
Q

Hamiltonian for the quantum harmonic oscillator in one dimension

A
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20
Q

Hamiltonian for the quantum harmonic oscillator in one dimension in terms of raising and lowering operators

A
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21
Q

Commutation relation of the raising and lowering operators

A
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22
Q

Spectrum of the harmonic oscillator

A
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23
Q

Virial theorem

A
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24
Q

Energy of a harmonic oscillator in 3 dimensions

A
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25
Q

Wavefunction and energy of a free particle

A
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26
Q

de Broglie relation

A

p = ℏk = h/λ

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27
Q

Normalization of the radial part of the wavefunction

A
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28
Q

Normalization of the angular part of the wavefunction

A
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29
Q

Angular momentum operator in x

A
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30
Q

Angular momentum operator in y

A
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31
Q

Angular momentum operator in z

A
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32
Q
A
33
Q
A
34
Q
A
35
Q
A
36
Q

Hamiltonian of the hydrogen atom

A
37
Q

Bohr radius

A
38
Q

Scale of the ground state hydrogen wavefunction

A
39
Q

Ground-state energy of a hydrogenic atom

A
40
Q

Excited-state energy of hydrogenic atom

A
41
Q

Fine structure constant

A
42
Q

de Broglie wavelength

A

λ = h / p

43
Q

Definition of a bra

A
44
Q

Bohr theory energy to remove an electron from a single-electron, multi-proton atom

A

E=Z2E1

45
Q

Products of operators [AB,C]

A

A[B,C] + [A,C]B

46
Q

Products of operators [A,BC]

A

[A,B]C + B[A,C]

47
Q

Raising/lowering normalization factors

A
48
Q

Δt

A

The amount of time it takes the expectation value of Q to change by one standard deviation

If any observable changes rapidly, the uncertainty in energy must be large.

49
Q
A
50
Q
A
51
Q

Spin raising and lower operators

A
52
Q

Blackbody power spectrum

A
53
Q

Stefan-Boltzmann law

A

dP / dA ∝ T4

54
Q

Wavelength of the peak of a blackbody spectrum, given by Wien’s displacement law

A
55
Q

Lz

A
56
Q

Sz

A
57
Q
A
58
Q
A
59
Q
A
60
Q

Range of possible values for Lz

A
61
Q

Number of allowed values for Lz

A

2l+1

62
Q

Range of possible values for Sz

A
63
Q

Range of possible values for Jz

A
64
Q

Range of possible values for Lq

A
65
Q

Range of possible values for Sq

A
66
Q

Range of possible values for Jq

A
67
Q

Selection rules for Δn

A

Δn = anything

68
Q

Selection rules for Δl

A

Δl = ±1

69
Q

Selection rules for Δml

A

Δml = 0, ±1

70
Q

Selection rules for Δmj

A

Δmj = 0, ±1

71
Q

ΔS’ selection rules for multi-electron atoms

A

ΔS’ = 0

72
Q

Special selection rule for J of multi-electron atoms

A
73
Q

Energies for particle in a box

A
74
Q

Number of electrons in each full subshell

A

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

2(2l+1) when s=1/2

75
Q

Energy of a particle in an infinite box

A
76
Q

Number of extrema in a harmonic oscillator wavefunction

A

n+1

77
Q

Symmetry of a wavefunction with odd n

A

anti-symmetric

78
Q

Symmetry of a wavefunction with even n

A

symmetric

Staudt Physics GRE (9 decks)

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