1. Calculate the transition ratio between the 2P-1S and 3P-2S states of the hydrogen.
2. Find the first order correction in the energy for the states n = 3 of the hydrogen atom subject to a constant electric field in the z direction (effect Stark). What are the states associated with each disturbed level?
If you can help me with any of this, or if you know a good quantum physiscs book where i can find this
1. To calculate the transition ratio between the 2P-1S and 3P-2S states of hydrogen, you would need to use the concept of selection rules and the energy level equations for hydrogen transitions.
The selection rules for electric-dipole transitions in hydrogen are:
- Δl = ±1, where l is the orbital angular momentum quantum number.
- Δm = 0, ±1, where m is the magnetic quantum number.
- Δn = ±1, where n is the principal quantum number.
The energy levels for hydrogen transitions are given by the equation:
E = -13.6 eV / n^2
To calculate the transition ratio, first find the energies of the initial (2P-1S) and final (3P-2S) states using the energy level equation. Then, calculate the ratio of the corresponding energy levels.
2. To find the first order correction in energy for states with n = 3 of the hydrogen atom subject to a constant electric field in the z direction (known as the Stark effect), you need to use the perturbation theory.
The first order correction in energy for the Stark effect is given by the formula:
ΔE₁ = <ψn|H'|ψn> = <ψn|qEz|ψn>
Here, E is the electric field, q is the electronic charge, and H' is the perturbation Hamiltonian associated with the electric field.
To find the states associated with each disturbed level, you can use the fact that the Stark effect splits the energy levels of the hydrogen atom and shifts them according to their quantum numbers. You'll need to calculate the new energies and determine the corresponding quantum numbers for the disturbed levels.
As for a good quantum physics book, "Principles of Quantum Mechanics" by R. Shankar is highly recommended as a comprehensive textbook that covers the fundamentals of quantum mechanics. Other popular books include "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili and "Quantum Mechanics and Path Integrals" by Richard P. Feynman and Albert R. Hibbs.