Consider the Spin Hamiltonian: Ĥ = -Aox where A e R is a non-negative real number. Use as a trial wave function: |(0)) = cos(0/2) |+z) + sin(0/2) |-z) (a.) What is the exact ground state and exact ground state energy for this Hamiltonian? (b.) Using the trial wave function, calculate E(0), the energy as a function of the parameter 0. (c.) Using the variational principle, estimate the ground state energy. How good is your solution and why?
Consider the Spin Hamiltonian: Ĥ = -Aox where A e R is a non-negative real number. Use as a trial wave function: |(0)) = cos(0/2) |+z) + sin(0/2) |-z) (a.) What is the exact ground state and exact ground state energy for this Hamiltonian? (b.) Using the trial wave function, calculate E(0), the energy as a function of the parameter 0. (c.) Using the variational principle, estimate the ground state energy. How good is your solution and why?
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![Consider the Spin Hamiltonian:
Ĥ = -AOT
where A E R is a non-negative real number. Use as a trial wave function:
|&(0)) = cos(0/2) |+z) + sin(0/2) |−z)
(a.) What is the exact ground state and exact ground state energy for this Hamiltonian?
(b.) Using the trial wave function, calculate E(0), the energy as a function of the parameter 0.
(c.) Using the variational principle, estimate the ground state energy. How good is your solution and why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F985cf4c3-8b0c-43d7-8bbe-1585000017f4%2F87c3e04e-ad8c-491d-b116-c110db221ef8%2F9nmcmb_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the Spin Hamiltonian:
Ĥ = -AOT
where A E R is a non-negative real number. Use as a trial wave function:
|&(0)) = cos(0/2) |+z) + sin(0/2) |−z)
(a.) What is the exact ground state and exact ground state energy for this Hamiltonian?
(b.) Using the trial wave function, calculate E(0), the energy as a function of the parameter 0.
(c.) Using the variational principle, estimate the ground state energy. How good is your solution and why?
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