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Equation of energy of a particle

  1. Jan 8, 2013 #1
    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....
    ..........................................
    for standing waves having ends with nodes, we have
    a=[itex]nλ/2[/itex]
    [itex]\Rightarrow[/itex] λ=[itex]2a/n[/itex]
    [itex]\Rightarrow[/itex] [itex]\nu[/itex]=v/λ
    [itex]\Rightarrow[/itex] E=h[itex]\nu[/itex]=nv/2a

    Now the particle has linear momentum as p=mv[itex]\Rightarrow[/itex]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[itex]\nu[/itex] is applicable for EM waves which has speed of light...Is this applicable if particle's speed is not equal to speed of light???
     
  2. jcsd
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