# Equation of energy of a particle

1. Jan 8, 2013

### justwild

Suppose a particle moves along Cartesian coordinates from x=0 to x=a, such that it can move in definite regions having definite energy which corresponds to formation of standing waves with nodes at its ends, that is, x=0 and x=a. Let the particle be of mass m and moving with velocity v.
Moreover, let n denotes the number of loops in the standing wave, which can take values 1,2,3...
....
Now I am deciding to derive the energy associated with the particle....
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for standing waves having ends with nodes, we have
a=$nλ/2$
$\Rightarrow$ λ=$2a/n$
$\Rightarrow$ $\nu$=v/λ
$\Rightarrow$ E=h$\nu$=nv/2a

Now the particle has linear momentum as p=mv$\Rightarrow$v=p/m , where p is the linear momentum which remains constant for a given energy level (I am using this as an analogy to angular momentum as per Bohr's postulates)

substituting in equation of energy we have,
E=np/2am

Now I have two questions...the analogy I have used for momentum...was that correct?
and E=h$\nu$ is applicable for EM waves which has speed of light...Is this applicable if particle's speed is not equal to speed of light???