1. Infinite-Potential Well Revisited V(x) V = 0 V = ∞ V = 0 L x = +5 x = 2 Consider the quantum mechanics of a particle with mass m that is confined in the infin
1. Infinite-Potential Well Revisited V(x) V = 0 V = ∞ V = 0 L x = +5 x = 2 Consider the quantum mechanics of a particle with mass m that is confined in the infin
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Transcribed Image Text:1. Infinite-Potential Well Revisited
V(x)
V = 0
V = 0
V = 0
L
x =
2
x = +5
2
Consider the quantum mechanics of a particle with mass m that is confined in the infinit
potential well of width L as shown above.
(a) By direct substitution into the time-independent Schrödinger,
h? d²µ(x)
+V(x)µ(x) = EÞ(x)
2m dx?
show that the wavefunction of the particle is
Pn(x) = Asin
+
with the quantized energy levels given by
h?n²n?
E = En =
2ml?
where n = 1,2,3, ...
Transcribed Image Text:(b) Does the wavefunction , (x) satisfy the appropriate boundary conditions?
(c) What is the value of the normalization constant A?
(d) Using the trigonometric identity
sin(a + B) = sin(æ)cos(ß) + cos(a)sin(ß)
show that w, (x) can be classified into wavefunctions with odd and even symmetries i.e.,
sin
п оdd
Un(x) = A{
cos
п еven
Expert Solution
Step 1
(b)
Introduction:
The finite potential well is an extension of the infinite potential well in which a particle is confined to a box, but one which has finite potential walls.
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