Answered: B. Evaluate T ý where is the normalized… | bartleby

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Consider a particle confined to a 1-dimensional box of length L
= 6 nm.
A. What is the probability of locating the particle between x = 3 nm and x = 3.2 nm in the ground state? 0.0664235
2.2
n?h?
B. Evaluate
where Y is the normalized particle in a box wave function. Express your answer in terms of h, m, n, and L.
6ml?
C. What is the potential energy operator equal to for PIAB?
1
10
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Question A3 Consider the energy eigenstates of a particle in a quantum harmonic oscillator with frequency w. a) Write down expressions for the energies of the three lowest states. b) c) Sketch the potential for this system, along with the position of the three lowest energy levels. Add to your sketch the form of the wavefunction and the probability density in the three lowest energy states. [10 marks]
3. A system of N harmonic oscillators of frequency w are prepared in identical initial states of wavefunction Þ(x,0). It is found that the measurement of the energy of the system at t = 0 gives 0.5hw with probability 0.25, 1.5hw with probability 0.5 and 2.5hw with probability 0.25. a. Write a possible function p(x, 0). b. Write the corresponding (x, t). c. What is the expectation value of the Hamiltonian in the state p(x,t) ? d. Calculate the expectation value of position at time t
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