Exam 2 Flashcards

1
Q

Does increase, decrease of stay constant as n is increased for a harmonic oscillator?

A

As n increased, increases since energy increases

higher energy => turning points out farther way => greater displacement on average

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2
Q

What does operating with the operator represent experimentally?

A

Equivalent to making a measurement of the corresponding physical quantity

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3
Q

What do the eigenvalues of a given operator represent in terms of the corresponding observable?

A

Represent allowed values for the result of the measurement

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4
Q

Why is is important to know whether or not two operators commute?

A

If two operators commute, the corresponding physical quantities can be known at the same time with nor uncertainty

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5
Q

Location where there is maximum probability of finding a particle

A

maximum => dY/dx = 0

cos(npix/a)=0

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6
Q

Location where there is zero probability of finding a particle

A

node => sin(npix/a) = 0

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7
Q

Quantum mechanical tunneling

A

When a particle lack sufficient energy to overcome a PE barrier but ends up on the other side anyway

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8
Q

How does the deBroglie wavelength of a particle affect the ability of the particle to tunnel?

A

A particle can tunnel a distance approximately equal to wavelength.
larger wavelength => easier to tunnel

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9
Q

Quantization

A

energy is discrete, not continuous

energy levels are like rungs on a ladder

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10
Q

Wave/particle duality

A

electrons, photons, etc behave as both waves and particles at the same time

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11
Q

What determines whether the rules of quantum mechanics or classical mechanics apply?

A

microscopic scale = quantum

macroscopic scale = classical

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12
Q

Where is the most probable location according to QUANTUM mechanics for a particle in the ground state of a 1D box?

A

In the center of the box

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13
Q

Where is the most probable location according to CLASSICAL mechanics for a particle in the ground state of a 1D box?

A

Equally likely everywhere

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14
Q

What happens to probability distribution by quantum mechanics as n is increased?

A

Looks more equally likely everywhere wine quantum mechanics must reduce to classical mechanics as n increases

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15
Q

Heisenberg uncertainty principle

A

Position and momentum cannot be known at the same time with no uncertainty
More precisely we know one the less precisely we know the other

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16
Q

What specific property of the probability distribution predicted from quantum mechanics is indicative of quantum mechanical tunneling?

A

probability of being past classical turning points is not zero since the wave function is not zero past turning points

17
Q

Where is the most probable location for a harmonic oscillator in quantum and classical?

A
quantum = at x=0
classical = at turning points