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Consider the bound states (E < 0) for the potential illustrated below: V(x) x < 0 Region I V(x) = 0 V(x) = -Vo 0 a Region III V(x) = -V, X = 0 X = a (a) this potential in regions I and II. Write down the form of the time-independent Schrödinger equation for (b) for the wave function for regions I and II. Define the constant l that relates to potential, energy, ħ, and mass of your particle for region I and define the constant k similarly for region II used in your solution. Determine the solutions to the time-independent Schrödinger equation (c) region I as much as possible. Employ the behavior as x goes to oo to simplify the solution for region II as much as possible. Employ the boundary condition at x = 0 to simplify your solution for (d) Next take those solutions and employ continuity at x = a. (e) Divide your two expressions derived in the previous part to express k in terms o1 l.

Consider the bound states (E < 0) for the potential illustrated below: V(x) x < 0 Region I V(x) = 0 V(x) = -Vo 0 a Region III V(x) = -V, X = 0 X = a (a) this potential in regions I and II. Write down the form of the time-independent Schrödinger equation for (b) for the wave function for regions I and II. Define the constant l that relates to potential, energy, ħ, and mass of your particle for region I and define the constant k similarly for region II used in your solution. Determine the solutions to the time-independent Schrödinger equation (c) region I as much as possible. Employ the behavior as x goes to oo to simplify the solution for region II as much as possible. Employ the boundary condition at x = 0 to simplify your solution for (d) Next take those solutions and employ continuity at x = a. (e) Divide your two expressions derived in the previous part to express k in terms o1 l.

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Consider the bound states (E < 0) for the potential illustrated below: V(x) x < 0 Region I V(x) = 0 V(x) = -Vo 0<x < a Region II II x > a Region III V(x) = -V, X = 0 X = a (a) this potential in regions I and II. Write down the form of the time-independent Schrödinger equation for (b) for the wave function for regions I and II. Define the constant l that relates to potential, energy, ħ, and mass of your particle for region I and define the constant k similarly for region II used in your solution. Determine the solutions to the time-independent Schrödinger equation (c) region I as much as possible. Employ the behavior as x goes to oo to simplify the solution for region II as much as possible. Employ the boundary condition at x = 0 to simplify your solution for (d) Next take those solutions and employ continuity at x = a. (e) Divide your two expressions derived in the previous part to express k in terms o1 l.
Transcribed Image Text:Consider the bound states (E < 0) for the potential illustrated below: V(x) x < 0 Region I V(x) = 0 V(x) = -Vo 0<x < a Region II II x > a Region III V(x) = -V, X = 0 X = a (a) this potential in regions I and II. Write down the form of the time-independent Schrödinger equation for (b) for the wave function for regions I and II. Define the constant l that relates to potential, energy, ħ, and mass of your particle for region I and define the constant k similarly for region II used in your solution. Determine the solutions to the time-independent Schrödinger equation (c) region I as much as possible. Employ the behavior as x goes to oo to simplify the solution for region II as much as possible. Employ the boundary condition at x = 0 to simplify your solution for (d) Next take those solutions and employ continuity at x = a. (e) Divide your two expressions derived in the previous part to express k in terms o1 l.
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