I need some help with this quantum mechanics question. In classical mechanics, we often solve problems by using Newton's second law F = ma to predict theposition r(t) of a particle subject to some known forces. Another common method is the energy method,whereby we use conservation of energy and the relation E = T + V between the total energy (E)and the kinetic (7) and potential (V) energies to predict the motion. Of course, the two methods arerelated because the force is related to the potential energy byFxdVdx(5.4) 1.A particle of mass m is in an infinite square well potential of width L, as in McIntyre'ssection 5.4. For all parts of this question, suppose we have an initial state vector |(t = 0)) =E₂), the 2ndenergy eigenstate. (This is also called "the 1st excited state", since E₁ is the loweststate or "ground state".)a) At t = 0, what is the expectation value of the energy? (Please answer in terms of m, L, andconstants of nature such as л and h.) Find the state vector at time t. What are the possibleoutcome(s) of an energy measurement now, with what probability(ies)? What is the expectationvalue of energy at time t? Hint: You do not need any wavefunctions for this part.b) Find the position probability density function at time t: [4(x, t)|².Use this tocompute (x(t)) for the above state. Is it time dependent? Is it physically reasonable? Why?c) Compute (p(t)). Does your answer make physical sense? Why?d) Calculate the probability that a measurement of position will find it somewhere betweenL/4 and 3L/4.e) Compute Ax and Ap for the above state, and comment on their product Axap. Feel free touse a computer for any integrals you find nasty. Recall from earlier this term how we define thestandard deviation:Ax = [y]x²|y) – (4[x]y}²

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I need some help with this quantum mechanics question. In classical mechanics, we often solve problems by using Newton's second law F = ma to predict theposition r(t) of a particle subject to some known forces. Another common method is the energy method,whereby we use conservation of energy and the relation E = T + V between the total energy (E)and the kinetic (7) and potential (V) energies to predict the motion. Of course, the two methods arerelated because the force is related to the potential energy byFxdVdx(5.4) 1.A particle of mass m is in an infinite square well potential of width L, as in McIntyre'ssection 5.4. For all parts of this question, suppose we have an initial state vector |(t = 0)) =E₂), the 2ndenergy eigenstate. (This is also called &#34;the 1st excited state&#34;, since E₁ is the loweststate or &#34;ground state&#34;.)a) At t = 0, what is the expectation value of the energy? (Please answer in terms of m, L, andconstants of nature such as л and h.) Find the state vector at time t. What are the possibleoutcome(s) of an energy measurement now, with what probability(ies)? What is the expectationvalue of energy at time t? Hint: You do not need any wavefunctions for this part.b) Find the position probability density function at time t: [4(x, t)|².Use this tocompute (x(t)) for the above state. Is it time dependent? Is it physically reasonable? Why?c) Compute (p(t)). Does your answer make physical sense? Why?d) Calculate the probability that a measurement of position will find it somewhere betweenL/4 and 3L/4.e) Compute Ax and Ap for the above state, and comment on their product Axap. Feel free touse a computer for any integrals you find nasty. Recall from earlier this term how we define thestandard deviation:Ax = [y]x²|y) – (4[x]y}²

Accepted Answer

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