Email me pchem questions and I'll post answers here.  Don't worry, I won't reveal your identity.

Question: For problem set #2, considering additional problem #1, I was wondering if you want a diagram similar to those shown in the text and if you would like the distance between the energy levels to be accurately represented.

I'm not sure what example you are referring to in the book, but Fig. 11.14 would be a good start.  Try to get the energy spacings reasonabely accurate and include the ground state (n = 1) and the limit for n = infinity.

Question: For problem set #2, additional problem 2, how would you like proof that we did this problem? Do you want a paper copy of the graph from the computer/calculator?

If you write a short program, you could supply the code.  It would be great to see your wave plotted for several different values of time, appropriately labeled from time point 1, time point 2, etc.  Include as much detail as you need to convey that you understand how the wave is generated.

For 11.12, I'm not really sure where to start because angular momentum is the momentum relating to theta, but I don't know what equation to use in order to derive an angular momentum.

Remember that in his model of the atom, Bohr proposed that angular momentum is quantized.  We discussed the detailed equation in class.  A great thing about quantum mechanics is that if you are in a state defined by a particular observable, angular momentum in this case, then you know the value of the observable.

For 11.14, I'm not sure what is meant by ionization potential. I know that ionization is removal of an electron, but looking through the chapters I can't seem to find anything that mentions ionization energy. Would I just use the Bohr prediction for emitted wavelength and calculate energy from that?

Ionization potential refers to the amount of energy required to move the electron from the particular quantum state (the ground state in this case) to an infinite distance from the nucleus.  Consider what quantum number you need to get the electron infinitely far from the nucleus.

Note: Hi Folks, Please take a look at the link at the bottom of our class page.  I created a link to a java applet that shows particle in a 1D box wavefunctions.  Enjoy!

For problems 11.28 and 11.29 on this week's homework, I'm not quite sure how to solve the second order differential equation, except by using the general solution equations such as the one you used in lecture yesterday (y=c1sin(kx) +c2cos(kx)).  Is this the best way to solve them or is there another way that you are looking for?  Additionally, are we expected to evaluate all of the constants in terms of C?

The main difference between the differential eqs. in probs 11.28 and 11.29 is the minus sign.  No, you don't need to follow a procedure for solving these equations.  Trial and error is fine.  Fortunately, as indicated by the hint in 28, you can limit your attempts to trig and exponential functions.  You should be able to write your final solution in terms of the constant C.  

For problem 11.26, I'm not sure how to calculate the velocity because the hint suggests that I should use the radius of the n=1 orbital and the angular velocity.

The linear velocity is the product of the angular  velocity and the radius.  Take a look at expressions from class relating the Bohr orbit momenta and the angular velocity, and also the expression for the radius R of the Bohr orbit.  Putting these together should allow you to determine the linear velocity.

To solve for the expectation value of the square momentum p² in the 3D box, would I just do p_x p_y and p_z separately and then multiply them all by each other?

There's a much more straight forward way to solve this, which we used in class for the 1D case.  Recall that p² = 2mH, where H is the Hamiltonian.  So just solve for the energy <E> and multiply by 2m.  Regarding the individual dimensions x, y, z, you could solve for p_x² and so forth, but you would add the squares, not multiply.

Nov 5
For 32b I just have a clarification question: For this problem I just have to set the integral of the complex conjugate equal to 1 and integrate with respect to theta from 0-pi?

Correct -- set the integral of ψ*ψ to unity and solve for N.  However, be sure to use the correct volume element for spherical harmonics.

For 50 I understand that the spacing is the spacing at equilibrium, but I'm a little confused about which equation I am using to calculate the spacing. I understand that I can calculate k/m using equation 12.145, but then do I use this in equation 12.142 ignoring the time?

Time-dependence is not really involved here.  The units for freq are s^-1 and refer to cycles per second.  Recall the relation E = hv. You are given the freq v, and just need to convert to energy.

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