Energy Levels of a Particle in 1 Dimension

[mkbh_10]

A particle in 1 dimension moves under the influence of a potential V(x)= a(x)^6 where a is constant. For larger n ,the quantized energy level depends on n as

E = (n)^3
E = (n)^4/3
E = (n)^6/5
E = (n)^3/2

 

[mkbh_10]

If i have md^2x/dt^2 = -dV/dx and calculate x(t) but after that where do i go?