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Quantum Mechanics > Quantum Mechanics (all topics) > Flashcards

Quantum Mechanics (all topics) Flashcards

1
Q

What is the equation for linear momentum?

A

p=mv

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2
Q

How is speed defined?

A

Magnitude of velocity

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3
Q

What is Newton’s second law of momentum?

A

rate of change of momentum is equal to force acting on the particle

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4
Q

What is acceleration?

A

Second derivative of r (position vector) with respect to time

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5
Q

What are equations for kinetic energy?

A

E=p^2/m=1/2mv^2

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6
Q

What are harmonic oscilator equations?

A

F=-kx
V=1/2kx^2
Etot=1/2mvmax^2

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7
Q

How is angular momentum J defined?

A

J=rxp (vector quantities)

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8
Q

For what type of radiation does classical mechanics fail?

A

Black body radiation

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9
Q

How is black body radiation defined?

A

An object capable of absorbing all frequencies of radiation uniformly

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10
Q

For what wavelengths does Raleigh-Jeans law fall short?

A

For short wavelengths

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11
Q

How can the experimental observation for black body radiation be rationalised?

A

By quantisation of energy

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12
Q

What evidence is there for the quantisation of energy apart from black body radiation?

A

Discrete absorption and emission spectra of atoms and molecules

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13
Q

What is the quantisation of energy equation?

A

E=nhv (permitted energies are integer values of hv)

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14
Q

How can light be described classically as a quantum description?

A

Classic: as a wave (EM)
Quantum: as particles called photons

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15
Q

What is the equation connecting the properties of waves?

A

lambda x v=c

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16
Q

Are EM waves transverse or longitudinal?

A

Transverse

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17
Q

What phenomena leads to diffraction?

A

wave interference

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18
Q

What experiment lead to the wave character of particles?

A

Davisson and Germer (1925)

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19
Q

What is the de Brogelie equation?

A

lambda = h/p

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20
Q

how is probability density related to the wave function?

A

absolute value squared

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21
Q

how are operator, eigenvalue and eigenfunction related?

A

operator x eigenfunction= eigenvalue x eigenfunction

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22
Q

what is the normalisation of the wave function?

A

probability density = 1

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23
Q

For a normalised wave function how do we obtain the expectation value?

A

w1 square modulus of c1 + w2 square modulus of c2 and so on…

24
Q

What is Heisenberg uncertainty principle?

A

It is impossible to state simultaneously the momentum and position of a particle

25
Q

What is the difference between fermions and bosons?

A

Bosons have symmetric wavefunctions

Fermions have anti-symmetric wavefunctions

26
Q

Give an example of a fermion and a boson?

A

Fermion: electron, neutron
Boson: helium atom, alpha particle

27
Q

What do l and m refer to?

A

l is orbital angular quantum number

m is magnetic quantum number

28
Q

How is m related to l?

A

permitted values of m are 2l+1

29
Q

What factors do radial wave functions depend on?

A

n and l but not (ml)

30
Q

Where do the two terms in the Veff equation come from?

A

columbic and centrifugal force

31
Q

What is a hydrogen atom?

A

a one electron atom or ion

32
Q

Describe the Stern-Gerlach experiment?

A

A beam of Ag atoms through a magnetic field. Two bands of Ag atoms observed. The observation led to the phenomenon being defined as ‘spin’.

33
Q

What are the spins of fermions and bosons?

A 
fermions = 1/2 integral spins
bosons= integral spins (including 0)
34
Q

What is needed to fully specify the state of a hydrogen atom?

A

n, l, ml and ms

35
Q

What are the selection rules for a photon?

A

delta l = +-1
deltaml = 0, +-1
Account for change in angular momentum occurring with emission of a photon

36
Q

Why is the SE for many electron atoms complex?

A

Interactions between electrons

37
Q

What is Pauli Exclusion Principle?

A

2 electrons per orbital and spins must be paired

38
Q

What is the Pauli exclusion principle in terms of fermions and bosons?

A

Fermions wavefunction changes sign when 2 labels of identical fermions exchanged.
Wavefunction stays the same for identical bosons

39
Q

What is Hund’s rule?

A

atom in its ground state maximises unpaired electrons

40
Q

Why is 4s orbital occupied before 3d?

A

The total energy is lower when this configuration is adopted

41
Q

How is shielding constant defined?

A

Z-Zeff

42
Q

How does Zeff arise?

A

From columbic repulsion of electrons. Equivalent to a negative point charge located at nucleus.

43
Q

How many triplet states are there?

A

3

44
Q

Which is lower in energy: triplet or singlet state?

A

Triplet state

45
Q

How does spin-orbit coupling arise?

A

From the interaction of the magnetic field created by orbital angular momentum and the magnetic moment created by orbital spin moment. Strength of coupling depends on orientation of momenta.

46
Q

What do orthohelium and parahelium refer to?

A

Parahelium is singlet state. Orthohelium is triplet state

47
Q

Is an antiparallel or parallel arrangement of ml and ms preferred?

A

Antiparallel maximises interaction

48
Q

What does J refer to? What are the values of J with regards to l

A

Total angular momentum and is a sum of ms and ml (vector sum can be represented by diagrams)
J=l+1/2 or l-1/2

49
Q

Does A (spin-orbit coupling constant) increase or decrease with atomic number, Z?

A

Increases, it increases with nuclear charge and hence atomic number Z. (Z^4 increase)

50
Q

Why are fine spectral lines observed for atoms?

A

Spin-orbit coupling gives rise to fine spectral lines

51
Q

Describe how term symbols are denoted for an atom?

A

multiplicity of term (2S+1), total orbital angular momentum (L) from Clebsch-Gordon series, total angular momentum (J) from Russell Saunders

52
Q

What happens the Russell-Saunders series for heavy atoms?

A

It fails in heavy atoms, as spin-orbit coupling is large and j-j coupling occurs.

53
Q

What S values give rise to a singlet, doublet and triplet?

A 
S=0 is singlet
S=1/2 is doublet
S=1 is triplet
54
Q

Where do selection rules arise for transitions?

A

Conservation of angular momentum and fact photon has spin 1 (boson)

55
Q

What are the quantum selection rules?

A

delta S= 0
delta L=0, +-1
delta J= 0, +-1

56
Q

Are selection rules for Russell-Saunders and what happens to heavier atoms?

A

Yes, for russell sanders. For heavier rules progressively fail, delta S= +-1 allowed therefore as j-j arises.

57
Q

How are transitions written?

A

Lower term to upper term

Quantum Mechanics (1 decks)

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