1. Consider a particle in one dimension with amplitude (x) given by V(x) = Aexp 242 Normalize this wavefunction. Hint: use this integral 00 -ax? dx a

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Chapter1: Units, Trigonometry. And Vectors
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1. Consider a particle in one dimension with amplitude (x) given by
V(x) = Aexp
242
Normalize this wavefunction. Hint: use this integral
00
-ax?
dx
a
2. Consider a particle of momentum p = 96hm-1. Here m stands for the unit
meters. What is the probability density of finding it at the position x?
3. Write the wavefunction
6Tx
v(x) = A cos
as the linear combination of wave-functions of definite momenta (Hint: you
need just two states of definite momentum).
4. Normalize the above wavefunction.
5. Plot the wavefunctions corresponding to the first three energy levels of a particle
in a box.
Transcribed Image Text:1. Consider a particle in one dimension with amplitude (x) given by V(x) = Aexp 242 Normalize this wavefunction. Hint: use this integral 00 -ax? dx a 2. Consider a particle of momentum p = 96hm-1. Here m stands for the unit meters. What is the probability density of finding it at the position x? 3. Write the wavefunction 6Tx v(x) = A cos as the linear combination of wave-functions of definite momenta (Hint: you need just two states of definite momentum). 4. Normalize the above wavefunction. 5. Plot the wavefunctions corresponding to the first three energy levels of a particle in a box.
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