uniform magnetic field B0
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At time t = 0, an electron and a positron are formed in a state with total spin
If interaction between the electron and the positron may be neglected, show that the spin Hamiltonian of the system may be written as Ĥ = ω0(Ŝ1z - Ŝ2z), where Ŝ1 is the spin operator of the electron, Ŝ2 is the spin operator of the positron, and ω0 is a constant. Show all work and explanations please
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- Consider a system spin-1/2 system, denoted by A, interacting with another system spin-1/2 system, denoted by B, such that the state of the combined system is AB) a++ B|-+). Find (a) the density matrix PA for system A corresponding to this state and (b) obtain the formulas for (()).QM 5.4 - Answer question throughly and with much detail as possible. -A positronium atom is a hydrogen-like atom with a positron (mass m = me, charge +e, spin 1/2) as a nucleus and an electron bound to it. The spin-spin interation of positronium can be described by a Hamiltonian H = A ~ 2 S1 · S2 Write down the energy levels of this system, according to the total spin S of the atom.
- -ax (ii) Show that Y, = A,e¯* is an eigenfunction of the simple harmonic 1 ocillator Hamiltonian above when a = 2h Vkm. Find the corresponding eigenvalue. Interpret the result.Please help meCalculate 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.Provide a written answerThe 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.