Consider a similar problem as above: a spin with two states | +1) and | -...
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Consider a similar problem as above: a spin with two states | +1) and | - 1). Let us define the Pauli matrices = (1 3). 0x = = Ty (5). 0 (1) Spin is a vector operator s = (x, y, z). The two states correspond to the column O vecotrs H = - 1 (9) -1 0% = + ¹) = (₁), √ − ¹) = such that s₂|+ 1) = (ħ/2)| +1) and s₂|-1) = (-ħ/2) | -1). In a magnetic field, the spin couples to the field via Zeeman coupling, with the Hamiltonian B.s 9HB ħ The magnetic field is along 45° direction in xy plane, i.e., B = B(1, 1, 0)/√2. (1) Find the eigen-energy and eigenstates of H. (2) Compute the average (s), i.e., each component (sa), (sy) and (sz), at temperature T. Consider a similar problem as above: a spin with two states | +1) and | - 1). Let us define the Pauli matrices = (1 3). 0x = = Ty (5). 0 (1) Spin is a vector operator s = (x, y, z). The two states correspond to the column O vecotrs H = - 1 (9) -1 0% = + ¹) = (₁), √ − ¹) = such that s₂|+ 1) = (ħ/2)| +1) and s₂|-1) = (-ħ/2) | -1). In a magnetic field, the spin couples to the field via Zeeman coupling, with the Hamiltonian B.s 9HB ħ The magnetic field is along 45° direction in xy plane, i.e., B = B(1, 1, 0)/√2. (1) Find the eigen-energy and eigenstates of H. (2) Compute the average (s), i.e., each component (sa), (sy) and (sz), at temperature T.
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To find the eigenenergy and eigenstates of the Hamiltonian H we need to diagonalize the matrix representing the Hamiltonian Lets calculate it step by ... View the full answer
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Business Forecasting with Forecast X
ISBN: 978-0073373645
6th edition
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