1

De Broglie relations state that for frequency $f$ and length $\lambda$ of a matter wave corresponding to (non-relativistic) particle of mass $m$, momentum $p$ and energy $E$ are given by: $$ \lambda=\frac{h}{p}$$ $$ f=\frac{E}{h}$$ It then follows that $$f=\frac{mv^2}{2h}=\frac{mv\cdot v}{2h}=\frac{p\cdot v}{2h}=\frac{h\cdot v}{\lambda\cdot 2h}=\frac{v}{2\lambda}. $$

But for wave with frequency $f$ and length $\lambda$, its speed $v_w$ is equal to $$ v_w=f\lambda$$ hence $$f=\frac{v_w}{\lambda} $$ It would therefore imply that $$\frac{v}{2\lambda}=f=\frac{v_w}{\lambda} $$ or $$ v_w=\frac{v}{2}.$$

It would therefore mean that the speed of de Broglie wave corresponding to a particle of speed $v$ would equal $v/2$... Is this correct? Does this make any sense?

0 Answers0