Question

Write down Schrodinger wave equation for a particle enclosed in infinite- square well potential and deduce expressions for energy Eigen values and normalized Eigen wave functions​

Answer 1

instead of knowing about Schrodinger wave equation first I explained about what it is

we learn that partical behaviour of electron and after that according to debrogli he explained that it behave both partical as well as wave

now in Schrodinger wave equation we learn probability of electron

we know that wave equation

y=a*sin2π(vt- x\lamda)

after (two time) differentiating this eqn with respect to X we get

d^2y/dx^2=-y4π^2/(lamda )^2______(1)

again with respect to t

we get

d^2y/dt^2=-y4,π^2*v^2/lamda^2____(2)

from 1and 2 on dividing

v^2*d^2y/dx^2=d^2y/dx^2

but this equation is capable only in a single plane but electron exist now in 3d and we assume it as a wave so sign sie is used instead of y so equation become

(d^2/dx^2+d^2\dy^2+d^2/dz^2)sie=1/u^2*d^2sie/dt^2(here d indicate del )