Exam 2 Flashcards
Does increase, decrease of stay constant as n is increased for a harmonic oscillator?
As n increased, increases since energy increases
higher energy => turning points out farther way => greater displacement on average
What does operating with the operator represent experimentally?
Equivalent to making a measurement of the corresponding physical quantity
What do the eigenvalues of a given operator represent in terms of the corresponding observable?
Represent allowed values for the result of the measurement
Why is is important to know whether or not two operators commute?
If two operators commute, the corresponding physical quantities can be known at the same time with nor uncertainty
Location where there is maximum probability of finding a particle
maximum => dY/dx = 0
cos(npix/a)=0
Location where there is zero probability of finding a particle
node => sin(npix/a) = 0
Quantum mechanical tunneling
When a particle lack sufficient energy to overcome a PE barrier but ends up on the other side anyway
How does the deBroglie wavelength of a particle affect the ability of the particle to tunnel?
A particle can tunnel a distance approximately equal to wavelength.
larger wavelength => easier to tunnel
Quantization
energy is discrete, not continuous
energy levels are like rungs on a ladder
Wave/particle duality
electrons, photons, etc behave as both waves and particles at the same time
What determines whether the rules of quantum mechanics or classical mechanics apply?
microscopic scale = quantum
macroscopic scale = classical
Where is the most probable location according to QUANTUM mechanics for a particle in the ground state of a 1D box?
In the center of the box
Where is the most probable location according to CLASSICAL mechanics for a particle in the ground state of a 1D box?
Equally likely everywhere
What happens to probability distribution by quantum mechanics as n is increased?
Looks more equally likely everywhere wine quantum mechanics must reduce to classical mechanics as n increases
Heisenberg uncertainty principle
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