Consider a step potential of height U0. U(x) = 0 if x < 0, U0 if x > 0 a.) A particle of energy ? > ?0 propagates from −∞ to +∞. Write down the form of the Hamiltonian operator when the particle is at x < 0. Do the same for the case when the particle is at ? > 0. b.) Solve for the eigenfunctions of the Hamiltonian for x < 0 and the Hamiltonian for x > 0. How many arbitrary constants are there? Apply the continuity condition(s) to find a relation among the constants to be determined.
Consider a step potential of height U0. U(x) = 0 if x < 0, U0 if x > 0 a.) A particle of energy ? > ?0 propagates from −∞ to +∞. Write down the form of the Hamiltonian operator when the particle is at x < 0. Do the same for the case when the particle is at ? > 0. b.) Solve for the eigenfunctions of the Hamiltonian for x < 0 and the Hamiltonian for x > 0. How many arbitrary constants are there? Apply the continuity condition(s) to find a relation among the constants to be determined.
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Consider a step potential of height U0.
U(x) = 0 if x < 0, U0 if x > 0
a.) A particle of energy ? > ?0 propagates from −∞ to +∞. Write down the form of the Hamiltonian operator when the particle is at x < 0. Do the same for the case when the particle is at ? > 0.
b.) Solve for the eigenfunctions of the Hamiltonian for x < 0 and the Hamiltonian for x > 0. How many arbitrary constants are there? Apply the continuity condition(s) to find a relation among the constants to be determined.
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