- #1

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## Main Question or Discussion Point

Hi, I'm extremely new to quantum mechanics (my only knowledge of quantum mechanics is that taught in physics C, ergo none, and a bit of wave mechanics... however I have a pretty strong mathematics background... diff-eqs + linear alg. + vector calc.), and was wondering as to how the derivation of

[tex]

\[

E = \hbar \omega \iff p = \hbar k

\]

[/tex]

worked. Here's my derivation, which seems encouraging, but could someone tell me where my derivation messed up?

[tex]

\[

E = \hbar \omega \iff \frac{1}{2} pv = \hbar \cdot 2 \pi f \iff

\frac{1}{2} p= \hbar \cdot \frac{2\pi}{\lambda} \iff p = 2 \hbar k \neq \hbar k

\]

[/tex]

[tex]

\[

E = \hbar \omega \iff p = \hbar k

\]

[/tex]

worked. Here's my derivation, which seems encouraging, but could someone tell me where my derivation messed up?

[tex]

\[

E = \hbar \omega \iff \frac{1}{2} pv = \hbar \cdot 2 \pi f \iff

\frac{1}{2} p= \hbar \cdot \frac{2\pi}{\lambda} \iff p = 2 \hbar k \neq \hbar k

\]

[/tex]