Solve the following problems. Write your solutions clearly and in detail in a short bond paper or yellow paper. 2. Symmetric Infinite Potential Well. A particle of mass m is confined in a symmetric potential well V(x) = { 0; -a ≤x≤ a ∞o; |x|> a (a) Write down the time-independent Schrödinger equation inside the well. (b) What is the general solution to the time-independent Schrödinger equation? (c) What are the boundary conditions? (d) Apply the boundary conditions to the general solution obtained in (b). Write down the corresponding equations. (e) From the equations in part (d), determine the allowed energies. Show that the even and odd energy levels can be generated separately from one another. (f) What are the normalized wave functions describing the state of the particle?
Solve the following problems. Write your solutions clearly and in detail in a short bond paper or yellow paper. 2. Symmetric Infinite Potential Well. A particle of mass m is confined in a symmetric potential well V(x) = { 0; -a ≤x≤ a ∞o; |x|> a (a) Write down the time-independent Schrödinger equation inside the well. (b) What is the general solution to the time-independent Schrödinger equation? (c) What are the boundary conditions? (d) Apply the boundary conditions to the general solution obtained in (b). Write down the corresponding equations. (e) From the equations in part (d), determine the allowed energies. Show that the even and odd energy levels can be generated separately from one another. (f) What are the normalized wave functions describing the state of the particle?
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Transcribed Image Text:Solve the following problems. Write your solutions clearly
and in detail in a short bond paper or yellow paper.
2. Symmetric Infinite Potential Well. A particle of mass m is confined in a symmetric potential well
0; -a ≤ x <a
∞o; |x|> a
V(x) = {
(a) Write down the time-independent Schrödinger equation inside the well.
(b) What is the general solution to the time-independent Schrödinger equation?
(c) What are the boundary conditions?
(d) Apply the boundary conditions to the general solution obtained in (b). Write down the
corresponding equations.
(e) From the equations in part (d), determine the allowed energies. Show that the even and odd
energy levels can be generated separately from one another.
(f) What are the normalized wave functions describing the state of the particle?
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