# Wave Equation (de Broglie)

Write the one dimensional wave equation and its solution.

Answer

The one dimensional associated de Broglie wave f(x) equation for a quantum particle of mass m is

-\hbar/(2m) *d^2 f(x)/dx + U(x)*f(x) = En*f(x) (Schrodinger Equation)

where $hbar$ is the Planck constant, U(x) the potential energy and En the eigenvalues of energy of that body (with which is associated the wave)

for a classical mechanical oscillator the equation rewrites as

d^{2 }f(x)/dx^{2} +(k/m) *f(x) = En*f(x)

where m is the mass of the oscillator and k the elastic constant of the spring (medium)

The general solution of the above equation is the wave function

f(x) = A*exp(i***k*****x**)= A*(cos(**kx**) +i*sin(**kx**))

where A is a constant value, **k** is the oscillator **wave** **vector **and **x** the **position** of the oscillator.