Combination of de Broglie wavelength and mass–energy equivalence gone wrong?I tried to combine the mass–energy equivalence for a particle with mass, E = ( m c 2 ) 2 + ( p c ) 2 = ( m c 2 ) 2 + ( γ m v c ) 2 with de Broglie wavelength, λ = h p = h γ m v .I get this equation: E = h c 2 λ v .This does not seem right, since the equations suggest the energy increases as the speed slow down which is not the case. But I can't see what I did wrong, either. Can someone help me?

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Combination of de Broglie wavelength and mass–energy equivalence gone wrong?I tried to combine the mass–energy equivalence for a particle with mass,  E  =      (    m          c      2              )      2        +    (    p    c          )      2        =      (    m          c      2              )      2        +    (    γ    m    v    c          )      2      with de Broglie wavelength,  λ  =            h      p        =            h              γ        m        v              .I get this equation:  E  =                    h                  c          2                            λ        v              .This does not seem right, since the equations suggest the energy increases as the speed slow down which is not the case. But I can&#039;t see what I did wrong, either. Can someone help me?

rotgelb7kjxw · Accepted Answer

Your algebra is correct:      1          λ      v        =            γ      m        h                h              c        2                    λ      v        =  γ  m      c    2    =  EYour interpretation,&quot;the equations suggest the energy increases as the speed slow down, which is not the case&quot;is not correct because both   v and   λ change as energy and velocity increase.

sg101cp6vv · Accepted Answer

The wavelength   λ cannot stay constant if the velocity   v changes. The question is &quot;do they change proportionally or not?&quot; A quick examination of your deBroglie wavelength relationship shows the following:  λ  v  =      h          γ      m        .We know that   γ is always greater than or equal to 1 and increases non-linearly with increasing   v. Therefore, your denominator in the final expression of   E is decreasing non-linearly as   v increases, resulting in an increasing energy.

Combination of de Broglie wavelength and mass–energy equivalence gone wrong? I tried to combine the

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