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Show that the angular wave number $k$ for a nonrelativistic free particle of mass $m$ can be written as $$ k=\frac{2 \pi \sqrt{2 m K}}{h} $$ in which $K$ is the particle's kinetic energy.

          Show that the angular wave number $k$ for a nonrelativistic free particle of mass $m$ can be written as $$ k=\frac{2 \pi \sqrt{2 m K}}{h} $$ in which $K$ is the particle's kinetic energy.
        

Added by Sarah T.

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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Show that the angular wave number $k$ for a nonrelativistic free particle of mass $m$ can be written as $$ k=\frac{2 \pi \sqrt{2 m K}}{h} $$ in which $K$ is the particle's kinetic energy.
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Transcript

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00:01 All right, so for a non -relativistic particle, what we have is that the kinetic energy is one -half mv squared, which can be rewritten as p squared over 2m.
00:11 And in quantum mechanics, the momentum of a particle can be written in terms of its wave number as, you know, planks reduced constant times the wave number.
00:22 And so our kinetic energy then is going to be equal to h squared, k squared, over 2m...
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