- #1
da_willem
- 599
- 1
Suppose you have a scalar field [itex]\psi(x,t)[/itex] subjected to a certain differential equation. Is there an easy way to find at which (phase) speed dx/dt this field propagates without actually solving the differential equation.
E.g. it is well known the differential equation
[tex]\frac{\partial^2 \psi}{\partial x^2} = \frac{1}{c^2} \frac{\partial^2 \psi}{\partial t^2}[/tex]
has solution with phase speed c
or that
[tex]\frac{\partial^2 \psi}{\partial x^2} = 0 [/tex]
has solutions with an infinite phase speed.
E.g. it is well known the differential equation
[tex]\frac{\partial^2 \psi}{\partial x^2} = \frac{1}{c^2} \frac{\partial^2 \psi}{\partial t^2}[/tex]
has solution with phase speed c
or that
[tex]\frac{\partial^2 \psi}{\partial x^2} = 0 [/tex]
has solutions with an infinite phase speed.