[benj]

i have these last two problems and i still can't figure it out..any help will be very much appreciated..pls..

1. the oscillation of the atoms around their equilibrium positions in the molecule HI can be modelled as a harmonic oscillator of mass m~m_H (the iodine atom is almost stationary) and the force constant k= 313.8 Nm^-1. evaluate the separation of the energy levels and predict the wavelength of the light needed to induce a transition between neighboring levels.
   ~my plan is to take the difference when v=0 and v=1 in E_v= (v+1/2)hw. for the next question i'll take the energy for v=0,equate it with h(frequency)..then solve for the wavelength....

2.(a) Confirm that the spherical harmonics Y_1,+1and Y_2,0 are solutions of the Schrodinger equation for a particle on a sphere,(b) Confirm by explicit integration that Y_1,+1 and Y_2,0 are normalized and mutually orthogonal.
    ~right now,i still have no idea..T_T..help meeehhhh..

pls...help..(~o~)

have a nice day!!!

[Mitch]

1) Sounds like a logical approach. However, I would use the wavelength of the difference in energy if v1-v2.

2) Here is a hint. In order to check whether something is normalized, you'll need to integrate it over all space and check if it equals 1.

[benj]

geesh..thanks for the tips..ok i'll get the wavelength from the energy difference(right?)...thank you very much...about being mutually orthogonal, is it right to integrate the product of the two harmonics and see if it equals zero??i dunno again..T_T

[benj]

uhm..my plan about the last question is to take the integral of the product of the two given harmonics (integrate it from teta=0 to teta=pi..and phi=0 to phi=2pi) and see if its zero..then for the normalization,i'll check if the the integral of each harmonic times its conjugate is equal to 1 for both harmonics..is this right??

[benj]

huhuhu..about the confirming of the two harmonics on whether they are solutions to the schrodinger eq,,,how do i do that???i'm still working on it but i cant figure it out yet..help me pls....

[Hunt]

uhm..my plan about the last question is to take the integral of the product of the two given harmonics (integrate it from teta=0 to teta=pi..and phi=0 to phi=2pi) and see if its zero..then for the normalization,i'll check if the the integral of each harmonic times its conjugate is equal to 1 for both harmonics..is this right??

Correct

[Hunt]

huhuhu..about the confirming of the two harmonics on whether they are solutions to the schrodinger eq,,,how do i do that???i'm still working on it but i cant figure it out yet..help me pls....

First find the two functions corresponding to the spherical harmonics. Next you substitute each into the schroedinger equation ( in angular form ) and solve to show that both are solutions. It's the same thing you do with algebraic equations except here you're plugging in a function Y=(Phi)(Theta) ( the spherical harmonic ) into a differential eq ( S.E. ).

~my plan is to take the difference when v=0 and v=1 in Ev= (v+1/2)hw. for the next question i'll take the energy for v=0,equate it with h(frequency)..then solve for the wavelength....

Your plan is good but you can also try to take in general the difference E(v+1) - E(v) and show that it is a constant for any v and then determine lambda. This is better and more general than taking E(1)-E(0).

[benj]

thank your very much for all the help..^^..geesh..thanks a million times sir Hunt and sir Mitch...thanks!!!happy holidays!!!