Quantum Mechanics & Atomic Physics Flashcards by Patrick Staudt

Q

Expectation value of an observable

A

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Q

Probability of finding a particle somewhere

A

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Q

Hermitian operator facts

A

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Q

position and momentum operators

A

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Q

Expansion coefficient

A

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Q

Expectation value in a superposition of states

A

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Q

Definition of inner product behavior under complex conjugation of a bracket

A

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Q

Applying an operator to a bracket

A

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Q

Inner product on a function space

A

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Q

Time dependent Schrödinger equation

A

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Q

Hamiltonian operator

A

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Q

A

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Q

Commutator of the position and momentum operators

A

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Q

Generalized uncertainty principle

A

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Q

Variance

A

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Q

Uncertainty of position and momentum

A

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Q

“Folklore” uncertainty of x and p

A

ΔxΔp ≈ ħ

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Q

“Folklore” uncertainty of energy and time

A

ΔEΔt ≈ ħ

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Q

Hamiltonian for the quantum harmonic oscillator in one dimension

A

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Q

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

A

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Q

Commutation relation of the raising and lowering operators

A

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Q

Spectrum of the harmonic oscillator

A

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Q

Virial theorem

A

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Q

Energy of a harmonic oscillator in 3 dimensions

A

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Wavefunction and energy of a free particle

de Broglie relation

p = ℏk = h/λ

Normalization of the radial part of the wavefunction

Normalization of the angular part of the wavefunction

Angular momentum operator in x

Angular momentum operator in y

Angular momentum operator in z

Hamiltonian of the hydrogen atom

Bohr radius

Scale of the ground state hydrogen wavefunction

Ground-state energy of a hydrogenic atom

Excited-state energy of hydrogenic atom

Fine structure constant

de Broglie wavelength

λ = h / p

Definition of a bra

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

E=Z²E₁

Products of operators [AB,C]

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

Products of operators [A,BC]

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

Raising/lowering normalization factors

Δt

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.

Spin raising and lower operators

Blackbody power spectrum

Stefan-Boltzmann law

dP / dA ∝ T⁴

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

L_z

S_z

Range of possible values for L_z

Number of allowed values for L_z

2l+1

Range of possible values for S_z

Range of possible values for J_z

Range of possible values for L_q

Range of possible values for S_q

Range of possible values for J_q

Selection rules for Δn

Δn = anything

Selection rules for Δl

Δl = ±1

Selection rules for Δm_l

Δm_l = 0, ±1

Selection rules for Δm_j

Δm_j = 0, ±1

ΔS' selection rules for multi-electron atoms

ΔS' = 0

Special selection rule for J of multi-electron atoms

Energies for particle in a box

Number of electrons in each full subshell

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

Energy of a particle in an infinite box

Number of extrema in a harmonic oscillator wavefunction

n+1

Symmetry of a wavefunction with odd n

anti-symmetric

Symmetry of a wavefunction with even n

symmetric