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
To calculate the transition ratio between the 2P-1S and 3P-2S states of hydrogen, you would need to consider the selection rules and the formula for the transition probability.
1. Selection rules: For an electric dipole transition in hydrogen, the selection rules are as follows:
- The change in orbital angular momentum (denoted as Δℓ) must equal ±1.
- The change in the principal quantum number (denoted as Δn) must be nonzero.
2. Transition probability formula: The transition probability (A) between two states can be defined as:
A = (2π/3ε₀ℏ²) |⟨final state|eˆ. r |initial state⟩|²
Where ε₀ is the electric constant, ℏ is the reduced Planck's constant, and eˆ . r represents the dot product of the electric dipole moment operator with the position vector.
For the 2P-1S transition, the initial state is the 2P state with ℓ = 1 and n = 2, and the final state is the 1S state with ℓ = 0 and n = 1.
For the 3P-2S transition, the initial state is the 3P state with ℓ = 1 and n = 3, and the final state is the 2S state with ℓ = 0 and n = 2.
To calculate the transition ratio, you need to compute the square of the transition probability for both transitions and then take the ratio of the two probabilities.
As for 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 (known as the Stark effect), you would need to consider the perturbation theory.
The first order correction in energy (ΔE₁) can be calculated using the following formula:
ΔE₁ = ⟨ψₙ| H' |ψₙ⟩
Where H' is the perturbation Hamiltonian (which describes the interaction with the electric field), and |ψₙ⟩ represents the unperturbed states of hydrogen with principal quantum number n = 3.
To find the states associated with each disturbed level, you would need to solve the Schrödinger equation with the perturbation Hamiltonian. The exact form of the perturbation Hamiltonian depends on the nature of the external electric field, such as a uniform field or a localized field.
As for a good quantum physics book, "Principles of Quantum Mechanics" by R. Shankar is highly recommended by many physicists. Another popular choice is "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili. These books cover a wide range of topics in quantum physics and provide comprehensive explanations and examples.