Quantum Mechanics Flashcards
(10 cards)
Why is a boundary condition need for particle on a ring?
To ensure the wave function is single valued, and so there are not multiple probabilities of being found on the same point of the ring
How can the boundary condition for Mj be proved for particle on a ring?
How does the angle dependence of a particle a rigid rotor vary?
And so if Mj= 0, no dependence, and so position unknown, momentum is known
With very large Mj, effectively a continuous spectrum spread out, unknown
For other values, some information of position known as momentum not completely known
How do you cauclate the energy differences between energy levels?
If usual, using energy level formula with n as the energy levels in question
If they give you a new formula, same principle but with this formula
What is the zero point energy of particle on a ring? And degeneracy?
Zero point energy when Mj=0
As when calculating the probability density, independent of the angle, and so position completely unknown, and some momentum can be known exactly, not violating the Heisenberg principle
Degenerate as multiple wave functions can have the same energy level
For a cubic box, how would you calculate the difference in the first and second energy level?
Not N=1 and N=2 for all
N=1 for the lowest, but then 2 x N=1 and 1 N=2 for the second
Then normal energy calculations
What is the energy level formula for 2D and 3d rotation?
What are orthogonal wave functions?
The product of these wave functions, when integrated across all range of values, is equal to 0
If normalising wavefunctions, when do you include the volume factor?
Not for particle in a box/oscillator as in cartesian
Yes for particle on a ring and hydrogenic orbitals, as reflected in the radial distribution function
