How Do You Solve a Potential in One Dimension Problem?

[Shafikae]

Can anyone help me with a problem. Please just answer whatever you can. Thanks. I have not started the problem because I don't know where to begin. I can solve physics problems but i just can't seem to start any of them off.

A classical particle of mass m moves in the presence of the following potential in one dimension:

V (x) = V0 [e^(-2γx) - 2e^(-γx) ]

(a) Find the minimum of the potential V and sketch the graph of V.

(b) Find the points of return depending on the energy. For which energies is the motion of m bounded?

(c) Expand V around its minimum up to second order and find corresponding approximation for the period of the oscillation.

 

[gabbagabbahey]

Can anyone help me with a problem. Please just answer whatever you can. Thanks. I have not started the problem because I don't know where to begin. I can solve physics problems but i just can't seem to start any of them off.

A classical particle of mass m moves in the presence of the following potential in one dimension:

V (x) = V0 [e^(-2γx) - 2e^(-γx) ]

(a) Find the minimum of the potential V and sketch the graph of V.

(b) Find the points of return depending on the energy. For which energies is the motion of m bounded?

(c) Expand V around its minimum up to second order and find corresponding approximation for the period of the oscillation.

Part (a) is just basic high school calculus. Surely you know how to find the minimum (or maximum) of a function?

For part (b), what is the definition of a "point of return"? What is true of the total energy for a bounded motion?

For part (c), just use a Taylor expansion (again, basic calculus!). Compare your result to the potential of a harmonic oscillator and use that to find the period.