Find the solutions of radial and angular parts of the 3D Hamiltonian of an hydrogen atom from a Atomic and Molecular Physics book. By looking at the radial wave functions, state if it is possible for an atomic electron to spend some of his time inside the nucleus.
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- 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 conduction electron is confined to a metal wire of length (1.46x10^1) cm. By treating the conduction electron as a particle confined to a one-dimensional box of the same length, find the energy spacing between the ground state and the first excited state. Give your answer in eV. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 AnswerWrite down the confi gurations for the ground states of calcium and aluminum. What are the LS coupling quantum numbers for the outside subshell electrons? Write the spectroscopic symbol for each atom
- 1. The Hamiltonian of the qubit in the standard basis is given by H = X⁰⁰ - X¹1 - ¡Xº¹ + ix¹⁰ (in units of eV). Find the possible values of the qubit energy E, and E₁ (in eV). Give the answer in decimals with accuracy to 3 significant figures.Consider the sheet formed by the intersection of the curves: x = 0, x = 4, y = 0, y = 3 [=] cm, with a variable density of mass per unit area ρ(x,y) = xy [=] g/cm2 . Write and evaluate multiple integrals to calculate the following: a. The area of the sheet [=] cm2 . b. The mass of the sheet [=] g. c. The shell moments about the x & y axes (Mx & My) [=] g∙cm. d. The position of the center of mass of the sheet ( , ) [=] cm.