- #1
mjda
- 13
- 0
I'm having trouble understanding how the 4-wave vector is derived, and also how it is then used alongside the 4-momentum vector to formulate the relativistic de Broglie equation.
The inner product of the 4-momentum vector with itself, is an invariant quantity. If we define the 4-momentum vector, P, as:
P = (p''' , iE/c) ---- where p''' is just the 3 dimensional momentum vector.
This then leads to finding:
P.P = p2 - (E/c)2 <-- this is invariant
The 4-wave vector, N, is defined as:
N = f (c/w , 1) <-- how does one derive this?
From what I have read, you should be able to derive the de Broglie equation by considering the inner product of P and N, with P.P?
The result being:
cP = hN
Has anyone seen this notation before and able to show this result is true? I can't find it anywhere in this form!
The inner product of the 4-momentum vector with itself, is an invariant quantity. If we define the 4-momentum vector, P, as:
P = (p''' , iE/c) ---- where p''' is just the 3 dimensional momentum vector.
This then leads to finding:
P.P = p2 - (E/c)2 <-- this is invariant
The 4-wave vector, N, is defined as:
N = f (c/w , 1) <-- how does one derive this?
From what I have read, you should be able to derive the de Broglie equation by considering the inner product of P and N, with P.P?
The result being:
cP = hN
Has anyone seen this notation before and able to show this result is true? I can't find it anywhere in this form!