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Hello,

I am having some difficulty with my Quantum Mechanics homework so I will post the questions and answer them to the best of my ability, which is still at a beginners level since this subject is new to me. I will update my answers as I figure them out. Any elaboration on the questions or my answers is greatly appreciated. Thank you.

The Hamiltonians do not depend on time.

If [tex]\Phi[/tex](x) is a solution, so is [tex]\Phi[/tex](-x).

I'm not sure how to approach this question.

A measurement for x is possible between its boundaries such as 0<x<a.

I'm not sure how to calculate the probability density.

I don't know.

No. <x> = a/2

No. E = n^2*pi^2*hbar^2 / 2*m*a^2

I don't know.

I am having some difficulty with my Quantum Mechanics homework so I will post the questions and answer them to the best of my ability, which is still at a beginners level since this subject is new to me. I will update my answers as I figure them out. Any elaboration on the questions or my answers is greatly appreciated. Thank you.

**1. Answer the following in brief sentences:**

a. The time independent Schrodinger Equation applies to only a particular class of systems. The Hamiltonians of all these systems have a common property. What is this property?a. The time independent Schrodinger Equation applies to only a particular class of systems. The Hamiltonians of all these systems have a common property. What is this property?

The Hamiltonians do not depend on time.

**b. If the Hamiltonian satisfies the equation: H(x) = H(-x), what can we say about the eigenfunctions of the Hamiltonian?**If [tex]\Phi[/tex](x) is a solution, so is [tex]\Phi[/tex](-x).

**c. A wave equation is solved and a relationship between the frequency [tex]\omega[/tex] and the wave number k (=2*pi/[tex]\lambda[/tex], with [tex]\lambda[/tex] being the wavelength) is obtained. A wave packet is formed using waves with k values near k0. What is the speed of the wave packet?**I'm not sure how to approach this question.

**2. Consider an Infinite one-dimensional potential well:**

A particle of mass m is released in the well at time t=0 with its initial state given by the wave function.

A particle of mass m is released in the well at time t=0 with its initial state given by the wave function.

**a. A measurement of its position is made, what are the possible results for x? For each measured value, what is the probability density?**A measurement for x is possible between its boundaries such as 0<x<a.

I'm not sure how to calculate the probability density.

**b. If instead of its position, its energy is measured, What are the possible results for E? For each measured value of E, What is the probability?**I don't know.

**c. Does <x (t)> depend on time? Calculate <x (t)>.**No. <x> = a/2

**d. Does <E (t)> depend on time? Calculate <E (t)>.**No. E = n^2*pi^2*hbar^2 / 2*m*a^2

**e. If the particle is in the ground state and its momentum is measured, what are the possible results of the measurement? What is the associated probability for each measured value?**I don't know.

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