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 Schr&ouml;dinger 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 pĀ² 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] [N.B. the integral ? sinĀ² x dx = Ā½ x - Ā¼ sin 2x] 

          1. Consider the 1D infinite square-well potential shown in the figure below.

V(x)
? ?
0 L x
Position

(a) State the time-independent Schr&ouml;dinger 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 pĀ² 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]
[N.B. the integral ? sinĀ² x dx = Ā½ x - Ā¼ sin 2x]
Show moreā€¦
1. Consider the 1D infinite square-well potential shown in the figure below. V(x) ? ? 0 L x Position (a) State the time-independent Schr ouml;dinger 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 pĀ² 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] [N.B. the integral ? sinĀ² x dx = Ā½ x - Ā¼ sin 2x]

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Consider the 1D infinite square-well potential shown in the figure below. (a) State the time-independent Schr&ouml;dinger 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 Ļˆ(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 pĀ² 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] [N.B. the integral āˆ« sinĀ² x dx = Ā½ x - Ā¼ sin 2x]
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Consider the 1D infinite square-well potential shown in the figure below. (a) State the time-independent Schr&ouml;dinger 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 Ļˆ(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 pĀ² 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] [N.B. the integral āˆ« sinĀ² x dx = Ā½ x - Ā¼ sin 2x]

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Transcript

-
00:01 So here we have been given us schrodinger functions.
00:04 Okay, so its functions looks like that up to the infinity.
00:09 And we have been asked the time independent function.
00:13 So this we can simply say that y should be equals to 10 theta times the x.
00:21 Okay, but here the x is 0.
00:24 So this is called our time independent function, okay, for the strutinger equation.
00:29 And the position so the energy so we know that this energy should be p squared by 2m for the particle but by uncertainty principle this p should be h cut over the delta x so this e will be h cut square over 2m times the x so this is our energy and it lies between 0 to l.
01:05 So this is the our first option.
01:11 Then we have the schrodinger equation...
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