Consider a particle at a central potential that has an orbital angular momentum l = 2h and a spin s = h. a) Find the energy levels with their respective degeneration, if the particle has a spin-orbit interaction as follows H50 = YL · Š, with y a constant.
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- What common charateristic do the lines in the Balmer series have? And fundamentally, why would any line in the hydrogen specctrum between 250nm and 700nm belong to the Balmer series?Electrons in a hydrogen atom are in a 3p excitation state transitioning radiative to energy level 2s. Taking into account the spin orbital interaction, determine : i) What is a spin orbit interaction?ii) Show the separation of 3p and 2s energy levels in the energy level diagramwithout an external magnetic field Biii) Show the separation of 3p and 2s energy levels in the energy level diagram due to the presence of an external magnetic field Biv) State the allowed transition conditionsv) Energy emitted when in space without a magnetic fieldvi) Energy emitted if it is in a space with a magnetic field B = 1Tplease solve part iThe un-normalized wave function for a negatively charged poin that is bound to a proton in an energy eigenstate is given by the equation in the provided image. b0 is a constant for this "pionic" atom that has the dimensions of length. What is the magnitude of the orbital angular momentum of the pion?
- A hydrogen atom is located in an area where there is both a uniform magnetic field and a uniform electric field that are parallel to each other. a) write out the Hamiltonian of perturbation (ignore the spin of the electron). b) use perturbation theory in order to calculate the first order correction to the energy levels n=1,2 c) is there any degeneracy left? Compare with situations in which there is a magnetic field or only an electric field.A spin-particle is in the spin state |A), described by the ket 7 i |4) = 5√2 tu) +5√2 tu). (a) Verify that A) is normalised. (b) Using the spinor representation (+₂) = ₁ | +) = √/2₁ 11³) = ₁ 1 +2) = [8] find the values of c₁ and c₂ for which |A) = C₁|1₂) + C₂l+₂). (c) If the observable S₂ is measured in the spin state |A), what values can be obtained and what are their probabilities? (d) Find the expectation value of S₂ in the spin state [A). (e) With reference to the properties of angular momentum, explain briefly how the results of the Stern-Gerlach experiment provide evidence of the existence of spin.Prove the angular momentum of a single electron..