Derive the commutation relationships for the x, y, and z components of the orbital angular momentum operator, as well as L².
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Q: Consider the case of atomic hydrogen placed in an uniform electric field. The shifts in the energy…
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Q: uniform magnetic field B0
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- Discuss how the Hamiltonian operator for the hydrogen atom was constructed.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.Please help me
- Calculate the 2nd order energy shift to the ground state energy of the one-dimensional harmonic oscillator, when a perturbation of the form H₁ = Є · (²) is added to the original Hamiltonian Ho = p²/2m+ ½ mw²x². Take a ⇒ (ħ/mw) ¹/2, the characteristic length scale of the oscillator. The second order correction to level n is given by E(2) = Σ m#n ||| H₁|v0| |2 m E(0) - EO)Spin/Field Hamiltonian Consider a spin-1/2 particle with a magnetic moment µ = -e/m$ placed in a uniform magnetic field aligned along the z axis. (a) Write the Hamiltonian for this system in matrix form. (b) Verify by explicit matrix calculation that the Hamiltonian does not commute with the spin operators in the r and y directions. Comment on how this affects the expectation values of these operators.A spin-2 system has 5 spin states in the Sz basis. Express the following as matrices or vectors in this basis: Ŝ2 operator, Ŝx operator, Ŝy operator, Ŝz operator, and State |2, 1⟩x (x component of spin = ħ).
- The following Hamiltonian describes spins in a magnetic field: Ĥ = ω0Ŝz.Show the following: the entangled state 1/√2 (|+z⟩1 |+z⟩2 + |−z⟩1 |−z⟩2) gets a relative phase at two times the rate that the independent spins would.Consider three noninteracting indistinguishable spin-0 particles trapped in a harmonic potential with energy states given as: [nx, Ny, nz). Consider three distinct single particle states: |0,0,0), |0,1,0), |0,2,0). Each of the particles can be in any one of the three states listed. How many different three particle states are possible?