A cavendish quantum mechanics primer exercise 1.6

5

I have been trying this question for the past couple days, and I just cannot seem to get it. I understand that the particle will end up accelerating and then decelerating and so on due to the direction of the different forces, but I just do not know how to start to put that into the maths. Can anyone please give me a hint on what to do?

https://isaacphysics.org/questions/qmp_ch1_q6?board=qmp_ch1_1_6

Reply 1

Eimmanuel

Study Forum Helper

15

Original post

by amamama0999

I have been trying this question for the past couple days, and I just cannot seem to get it. I understand that the particle will end up accelerating and then decelerating and so on due to the direction of the different forces, but I just do not know how to start to put that into the maths. Can anyone please give me a hint on what to do?

https://isaacphysics.org/questions/qmp_ch1_q6?board=qmp_ch1_1_6

The hint is in Quantum Mechanics Primer Ex. 1.2.
Use the result for Ex1.6.

Reply 2

amamama0999

OP

5

It is what happens at the step that is confusing me. The depth of the well is 4V_0 up to x=a, then the depth of the well is 2V_0. In either case, the resultant energy of the particle is just V_0. This is my calculation, but it is obviously logically wrong. What is the actual energy?

Reply 3

Eimmanuel

Study Forum Helper

15

Original post

by amamama0999

It is what happens at the step that is confusing me. The depth of the well is 4V_0 up to x=a, then the depth of the well is 2V_0. In either case, the resultant energy of the particle is just V_0. This is my calculation, but it is obviously logically wrong. What is the actual energy?

Define your actual energy.

Reply 4

amamama0999

OP

5

I meant what is the resultant energy? E-depth of potential well

Reply 5

Eimmanuel

Study Forum Helper

15

Original post

by amamama0999

It is what happens at the step that is confusing me. The depth of the well is 4V_0 up to x=a, then the depth of the well is 2V_0. In either case, the resultant energy of the particle is just V_0. This is my calculation, but it is obviously logically wrong. What is the actual energy?

Original post

by amamama0999

I meant what is the resultant energy? E-depth of potential well

I would recommend that you get the Quantum Mechanics Primer book to understand some of the fundamental physics and the book provides hints in solving some of the problems. Some of the problems are also solved in the book with missing maths.
I would discourage you to use or invent unscientific terms like “resultant energy” or “E-depth” to hinder your understanding and your communication with other.

If you have solved Ex. 1.2, Ex. 1.6 is purely an extension. If you have not solved or don’t know how to solve Ex. 1.2, please say so or else you would be going in circle.

The problem in Ex. 1.6 is potential well with steps (like a staircase).
In Ex.1.2, if you have done the problem correctly, you should know that in Ex.1.6,
from x=0 to x=a, the “potential energy” is zero,
from x=a to x=3a/2, the “potential energy” is 2V_0,
from x=3a/2 to x=∞, the “potential energy” is 4V_0.
where V_0 is just a numerical constant.

What you need to consider is that the total mechanical energy E=3V_0 is constant,
PE + KE = E -----(1)
KE = E - PE ----- (2)
Apply (2) to find the different “average speed” at “different steps”.

With the average speed, you can proceed to find the time taken to traverse from x=0 to x=3a/2 and finally the period. This is what Ex. 1.2 should have taught you.