The differential equation is #(dphi)/dx+kphi=0# where #k=(8pi^2mE)/h^2#E,m,h are constants.Find what is #(h/(4pi))# If #m*v * x ~~(h/(4pi))#?

1 Answer
Feb 4, 2018

Answer:

The General Solution is:

# phi = Ae^(-(8pi^2mE)/h^2x) #

We cannot proceed further as #v# is undefined.

Explanation:

We have:

# (dphi)/dx + k phi = 0 #

This is a First Order Separable ODE, so we can can write:

# (dphi)/dx =- k phi #
# 1/phi \ (dphi)/dx =- k #

Now, we separate the variables to get

# int \ 1/phi \ d phi = - int \ k \ dx #

Which consists of standard integrals, so we can integrate:

# ln | phi | = -kx + lnA #
# :. |phi| = Ae^(-kx) #

We note that the exponential is positive over its entire domain, and also we have written #C=lnA#, as the constant of integration. We can then write the General Solution as:

# phi = Ae^(-kx) #
# \ \ = Ae^(-(8pi^2mE)/h^2x) #

We cannot proceed further as #v# is undefined.