Question

1. Consider the 1D infinite square-well potential shown in the figure below. V(x) ? ? 0 L x Position (a) State the time-independent Schrödinger equation within the region 0 < x < L for a particle with positive energy E. [2 marks] (b) The wavefunction for 0 < x < L can be written in the general form ?(x) = A sin kx + B cos kx. Find the normalised wavefunction for the 1D infinite potential well. [3 marks] (c) Determine the expectation values of x, p and p² of a particle in the first excited state of an infinite square-well potential. [3 marks] (d) Sketch the wavefunction, probability densities and energy levels of the first three levels of the infinite square well potential and discuss in relation to your answers in part (c). [2 marks]

          1. Consider the 1D infinite square-well potential shown in the figure below.
V(x)
?
?
0
L
x
Position
(a) State the time-independent Schrödinger equation within the region 0 < x < L for a particle with positive energy E.
[2 marks]
(b) The wavefunction for 0 < x < L can be written in the general form
?(x) = A sin kx + B cos kx.
Find the normalised wavefunction for the 1D infinite potential well.
[3 marks]
(c) Determine the expectation values of x, p and p² of a particle in the first excited state of an infinite square-well potential.
[3 marks]
(d) Sketch the wavefunction, probability densities and energy levels of the first three levels of the infinite square well potential and discuss in relation to your answers in part (c).
[2 marks]

1. Consider the 1D infinite square-well potential shown in the figure below.
V(x)
?
?
0
L
x
Position
(a) State the time-independent Schrödinger equation within the region 0 < x < L for a particle with positive energy E.
[2 marks]
(b) The wavefunction for 0 < x < L can be written in the general form
?(x) = A sin kx + B cos kx.
Find the normalised wavefunction for the 1D infinite potential well.
[3 marks]
(c) Determine the expectation values of x, p and p² of a particle in the first excited state of an infinite square-well potential.
[3 marks]
(d) Sketch the wavefunction, probability densities and energy levels of the first three levels of the infinite square well potential and discuss in relation to your answers in part (c).
[2 marks]

Added by William C.

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