Use the variational trial function Ψ Y 10 r exp cr 2 to calculate the total

# Use the variational trial function ψ y 10 r exp cr 2

• 3

This preview shows page 1 - 3 out of 3 pages.

The non-linear variational method applied to the hydrogen atom. Use the variational trial function: Ψ = Y 10 r exp cr 2 ( ) to calculate the total energy of the hydrogen atom via the following steps: (a) From your knowledge of the exact solutions of the hydrogen atom, explain which state this trial function will be modeling, and why.

Subscribe to view the full document.

(b) Obtain an expression for the energy in terms of the variational parameter, c . Make a plot of the energy versus c for values of c that range between obviously too small (e.g. starting with 0.1), and obviously too large (e.g. ending with 10), adjusting so that the plot provides useful visual information. (c) Find the optimum value of the parameter c that minimizes the energy, and the associated energy, and compare with the known exact value for H. (d) Discuss why values of c that are too small lead to energies that are too high. Also discuss why values of c that are too large lead to energies that are also too high! 3. The linear variational method applied to the perturbed particle in a box. For simplicity we will work in reduced units where the box size is L =1, the mass is m =1, and for convenience, ! =1 (these are atomic units). We recommend that you use the TA- supplied Python scaffold. Your objective is to develop approximate solutions to the following potential: V x ( ) = x ; x [0,1 2] V x ( ) = 1 x ( ) ; x [1 2,1] Your linear variational wavefunctions will be a superposition of N unperturbed particle-in-a-box states, where you will be able to optimize the coefficients a given N ,
• Summer '16
• Alistair Sinclair

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes