# Extensions to equations of physical quantities of quantum mechanical matter waves

## Author information

Author: Charles Ewan Milner

## Abstract

This paper explores the manipulation of equations for physical quantities of quantum mechanical matter waves which reveals interesting formulas for these quantities that use common physical quantities.

## Main Paper

In this paper, the following symbols shall represent their assigned physical quantities:

- ${\displaystyle h}$  – Planck constant (Ratio of the energy of a quantum mechanical wave to its frequency and product of the momentum of a matter wave and its wavelength)

- ${\displaystyle f}$  – Matter wave frequency

- ${\displaystyle \lambda }$  – Matter wavelength

- ${\displaystyle E}$  – Matter wave energy

- ${\displaystyle v}$  – Matter wave speed

- ${\displaystyle p}$  – Matter wave momentum

This paper shall use the well-known equations of physical quantities of general quantum mechanical and matter waves ${\displaystyle v=f\lambda }$ , ${\displaystyle E=hf}$ , and ${\displaystyle p={\frac {h}{\lambda }}}$ . These equations can be manipulated to show alternative expressions for certain physical quantities of those waves. It can be found that:

${\displaystyle {\frac {E}{p}}={\frac {hf}{\frac {h}{\lambda }}}=hf\cdot {\frac {\lambda }{h}}={\frac {hf\lambda }{h}}=f\lambda =v}$ ,

${\displaystyle E={\frac {E}{p}}\cdot p=vp}$ ,

${\displaystyle {\frac {E}{v}}={\frac {vp}{v}}=p}$ ,

${\displaystyle {\frac {E}{\lambda }}={\frac {E}{\frac {v}{f}}}=E\cdot {\frac {f}{v}}={\frac {Ef}{v}}={\frac {vpf}{v}}=pf}$ ,

and

${\displaystyle {\frac {p}{v}}={\frac {\frac {E}{v}}{v}}={\frac {E}{v}}\cdot {\frac {1}{v}}={\frac {E}{v^{2}}}}$ . These equations show formulas for several physical quantities of quantum mechanical matter waves that can be expressed in alternative ways to well-known ones and use common physical quantities as part of them.

These equations show formulas for several physical quantities of quantum mechanical matter waves that can be expressed in alternative ways to well-known ones and use common physical quantities as part of them.