Using the principle of conservation of energy

[Just_some_guy]

Hi all,

I'm not 100% sure this belongs in this topic but it was a problem I was given in a quantum mechanics lecture so here goes, sorry if I am wrong.Anyway I was given a hamiltonian H= T+VWhere T is kinetic energy and av is potential, and asked to use

dH/dt= 0

to find an analogy between it and Newtons laws, now my work is far to long to post using the usual method so I have attached a photograph of all my work I hope it is clear what I have done, I just want to know if this is the correct approach or I have somehow magically confused myself into what seems to be a reasonable answer :)

Thanks for any help

 

[vela]

now my work is far to long to post using the usual method so I have attached a photograph of all my work

Let's be honest. It's not too long; you're just too lazy to type it in.

 

[Just_some_guy]

Ok fair enough! I'm using u phone so I find it much better to post photographs

 

[BvU]

V = V(x) so ${\partial V\over \partial t} = 0$. However, that's not what you have in your relevant equation. From that (and from any first-grader dimensional analysis) you want ${\partial V\over \partial x}$ there. Coming close to Newton already ?

 

[Just_some_guy]

So potential between that a and 0 is not 0?

 

[Just_some_guy]

I'm not sure I follow what you are saying?

 

[vela]

He's saying there's a mistake in the fifth line of your work.

 

[Just_some_guy]

Ah I see it! I have dV(x)/dt

Rather than what I should have which is

dV(x)/dx