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Phys108 > 330 terms > Flashcards

330 terms Flashcards

1
Q

Normalization

A

Finding A (amplitude) of a soln to the Schrodinger equation since the sum of all the probabilities must be equal to 1

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2
Q

Zeeman effect

A

Describes how the energy of an electron changes in the presence of an electric field

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2
Q

What does m quantum number refer to ?

A

Magentic property

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2
Q

Hartree Fock approximation aka orbital approximation

A

Mathimatically assumes that each electron has its own wavefunction and that the total wavefunction is a seperable product of inidividual wavfunctions

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3
Q

Issues with HF approx

A

HF ALWAYS overestimates energy!

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3
Q

Zero point energy

A

The zero point energy is the ground state energy for the harmonic oscillator E=h(nu). Given the uncertainty principal , if E=0 here, then there would be certain position and certain momentum (since velocity=0).

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3
Q

Postulate 1 of Quantum mechanics

A

All the info ab a quantum mechanical system is contained in the wavefunction
psi is an indepterminate model (psi cannot predict the future)

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4
Q

Postulate 2 of Quantum mechanics

A

Every observable in classical mechanics corresponds with a linear operator
a linear operator is distributive
psi must be single valued,continuous, finite,
(end behavior that gpes to zero)

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5
Q

Postulate 3 of Quantum mechanics

A

Any measurement associated with an observable associated with the operator A, only values that can ever be observed are the eigenvalues from A psi =a psi

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6
Q

Postulate 4 of Quantum Mechanics

A

The average value for any observable is <a>= (integral over all space) psi (complex conj) * Ahat * psi</a>

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7
Q

If you constrain a wave you get

A

Quantized states! can on get interger values of full wavelengths that fit between 2 points.

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8
Q

What to orbitals represent?

A

Probabilites that you find an electronin an area in space

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9
Q

A typical molecule has ___ degrees of freedom

A

3N-6 internal (vibrational degrees of freedom)

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10
Q

Anharmonicity

A

asymetric potential

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11
Q

Pauli principal arrise from 2 properties of e-

A

1) electrons are indistinguisable
2) electrons are

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12
Q

Born Oppenhiemer approximation

A

electrons treat nuclei as frozen and fixed
nuclei see electrons as delocalized
this assumption allows us to multiply electron energy and nuclear energy

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13
Q

Define Hermitian

A

Hermitian means A operator operating on complex conjugate is equal to A operating on the function

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14
Q

Eigenfunctions of the Hermitian operator

A

MUST be real (not imaginary) because all obeservables are observable

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14
Q

Commutator

A

When 2 operators commute they can be simultaneously defined for a system

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15
Q

Orthogonal definition

A

Independent or not overlapping,
can use symmetry argument:

16
Q

Why wavelength and frequency inversely related?

A

Frequency quantifies the energy per photon
(we could also increase the number of the photons)

17
Q

Photoelectric effect

A

Ephoton= threshold energy + KE (0.5 mv^2)

18
Q

de Broglie wavelength

A

=h/p=h/mv
we can determine the wavelength of a piece of matter

19
Q

How does treating matter as wave lead to quantized states ?

A

Because you contrain a wave such that interger values of the wavelength exist between 2 points

20
Q

Uncertainty for PIB

A

position
momentum

21
Q

Linear operators

A

Position : x(hat)= x
Momentum: p(hat)=-ih(bar) d/dx
Kinetic Energy: T(hat)= -h^2/2m d^2/dx^2
Energy: Hamiltonian

22
Q

Resonance criteria

A

If energy of light wave matches the frequency of chemical processes (spacing of energy levels), then the light can be absorbed

23
Q

Limitation of PIB (from pset)

A

-the repulsion of other electrons in the system
-ignores nuclei
-finite walls (molecule can be oxidized)

24
Q

EM spectrum

A

low E
radiowave (excites spin)
microwave (excites rotations)
IR (excites molecular vibrations and nuclear motions)
Vis/Uv (excites electrons)
high E

25
Q

Postulate 4 QM

A

average value is the integral (over all space) of psi* A psi

26
Q

Postulate 5 QM

A

Time independent Schrodinger equation

27
Q

All Qm operators must be

A

Hermitian

28
Q

Eigenfunctions of any hermitian operator must be

A

orthogonal

29
Q

Tunneling region

A

Intersection of V(x) and the eigenstate, particle can “jump” over an energy barrier

30
Q

Vibrational degrees of freedom

A

3N-6 for to specify the conformation of bc we subtract away rotations and traslations that don’t change bond length

31
Q

Transition states

A

Most unstable, 3N-7 degees of freedom
force constant is negative, and so there is an imaginary frequency meaning that the molecule cannot oscillate, so that it cannot feel a restoring force and so a slight distruption to the bond pushes the molecule to fall to stable product

32
Q

Rigid Rotor

A

answers following question: what are the likely angular rotations of a diatomic molecule

33
Q

Assumptions of RR model

A

-Fixed bond length and so as a result mass is constrained to live somewhere on a 2D surface of a sphere
-center of mass coordinates

34
Q

order of magnitude for visible light spectrum

A

400nm-700nm

35
Q

Frequencies of visible light

A

10^-14 to 10^-15

36
Q

I (moment of inertia)

A

I= μR^2

37
Q

Reduced mass

A

m1*m2/(m1+m2)

38
Q

Frank Condon Principal

A

Over the course of excitation, nuclei do not move

39
Q

Microwave spectrum (rotational energy) features

A

-regularly spaced CHANGE in energy levels
-gap in middle- fundemental frequency
-R- branch peaks closer together than P branch (positive delta J) peaks

40
Q

Angular momentum (Lx, Ly, Lz) and L^2)

A

Can only define one component at a time(carves out curve of uncertainty)
ONE exception to this is when L^2 is zero- then each component is zero but for the uncertainty prinicpal to be met ther must be uncertainty in postion (spherical so knoe r but could be anywher on the surface)

41
Q

Only model with regularly spaced energy levels?

A

The 1D harmonic oscillator

42
Q

Why HF a not great approximation?

A

e- are moving to the average of the other postion (lots of unceratinty) so HF is always an over approximation

43
Q

Average position of PIB graphically?

A

Where psi squared is symmetric

44
Q

Can superpostion for H atom have well defined energy?

A

Yes- in the case of degereracy- ex psi 200 and psi 211 , both have the same energy

Phys108 (6 decks)

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