c) Find the commutator relation 1) [L², Lx] 2) [H,z]
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![c) Find the commutator relation
1) [L², Lx]
2) [H,z]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b8701d9-f318-4b09-8ec8-11f03c4d69ec%2F3cb54d45-ca09-444f-bb95-a1492a7a8104%2Fqda53ja_processed.png&w=3840&q=75)
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- da=do= 4) For the following d hydrogenic wavefunctions, find the magnitude and the z component of the orbital angular momentum. You can give your results in terms of h. اور اہل = 1 √2 16t i√2 i√2 Final (d₁2+ d_2) = (165) R₁2(r) (x²- y²)/r² 151/2 1/2 R₁2(r) (3cos²0-1)=(16) R2(1)(32²-7²)/² 1/2 (d+2-d-2)= (15) Rm2(7)xy/² =(d. 1+d-1)= (d_1-d-1)=- 1/2 1/2 (15) R₁2 (r)yz/r² 10 June 2011 1/2 (45) * Ru2(1) 2x/r²please answer c) only 2. a) A spinless particle, mass m, is confined to a two-dimensional box of length L. The stationary Schrödinger equation is - +a) v(x, y) = Ev(x, y), for 0 < r, y < L. The bound- ary conditions on ý are that it vanishes at the edges of the box. Verify that solutions are given by 2 v(1, y) sin L where n., ny = 1,2..., and find the corresponding energy. Let L and m be such that h'n?/(2mL²) = 1 eV. How many states of the system have energies between 9 eV and 24 eV? b) We now consider a macroscopic box (L of order cm) so that h'n?/(2mL?) ~ 10-20 eV. If we define the wave vector k as ("", ""), show that the density of states g(k), defined such that the number of states with |k| between k and k +dk is given by g(k)dk, is Ak 9(k) = 27 c) Use the expression for g(k) to show that at room temperature the partition function for the translational energy of a particle in a macroscopic 2-dimensional box is Z1 = Aoq, where 2/3 oq = ng = mk„T/2nh?. Hence show that the average…How to evaluate the 2 partial derivatives from the expression for Z?
- 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.Mathematical Physics 3 Topic: Rotations of Functions and Angular Momentum1. 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.2(6) Calculate the fundamental vibrational wavenumber (in cm-1) for HI molecule, if its angular vibrational frequency is 4.394×1014 s-1. Calculate the vibrational energy of the molecule in the ground state and the force constant. Assume the mass is the mass of a proton.