- #1
SpaceNerdz
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- TL;DR Summary
- I've been trying to derive ω = E/hbar, but to no success. I thought it was fairly straight forward derivation, could some one point out my mistake ?
OK, so I just want to show ω = E/h = kv, but I keep running into errors, I don't know why.
So, let's start with momentum:
p^2 / 2m = E
p^2 = 2mE
p = sqrt(2mE)
h/λ = sqrt(2mE)
hk = sqrt(2mE)
k = sqrt(2mE)/h
So far so good. Now let's start with conserved Energy
E= ½ mv^2
2E/m = v^2
v = sqrt(2E/m)
So, the angular velocity is :
ω = kv
ω = sqrt(2mE)/h *. sqrt(2E/m)
ω = 2E/h
E = ½hω
This is weird. Where did the ½ come from ?
I thought its E =hω.
Can someone tell me where I went wrong ? I'm pretty sure the algebra is correct, but am I introducing some concept where I shouldn't ? Please let me know !
So, let's start with momentum:
p^2 / 2m = E
p^2 = 2mE
p = sqrt(2mE)
h/λ = sqrt(2mE)
k = sqrt(2mE)/
So far so good. Now let's start with conserved Energy
E= ½ mv^2
2E/m = v^2
v = sqrt(2E/m)
So, the angular velocity is :
ω = kv
ω = sqrt(2mE)/
ω = 2E/
E = ½
This is weird. Where did the ½ come from ?
I thought its E =
Can someone tell me where I went wrong ? I'm pretty sure the algebra is correct, but am I introducing some concept where I shouldn't ? Please let me know !