1. The problem statement, all variables and given/known data A particle of mass m moves in 3-d in the potential well [tex] V(r)=-V_0 [/tex] at [tex] r<r_0[/tex] where [tex] V0 [/tex] and [tex]r_0[/tex] are positive constants. If there exists a state in which the particle is bound to the potential well, the wave function for the bound state with the lowest energy is spherically symmetric and the radial wave satisfies equations [tex] -h-bar^2/2m*(d^2/dr^2)*u(r)+V(r)*u(r)=Eu(r)[/tex] [tex] u=\varphi*r[/tex] Find the minimum value of the depth [tex] V_0 [/tex] for which there exists a bound state. (recall that the radial function satisfies the condition u(0)=0 , because [tex]\varphi[/tex](r)= u(r)/r has to be regular at the origin 2. Relevant equations [tex] -h-bar^2/2m*(d^2/dr^2)*u(r)+V(r)*u(r)=E*u(r)[/tex] [tex] r^2=(x^2+y^2+z^2) [/tex] 3. The attempt at a solution I don't know what they mean when they state ' [tex]\varphi[/tex](r)= u(r)/r has to be regular at the origin'; I don't know why they want you to find a minimum value for V_0 since it is already given in the problem Should I apply seperation of variables where [tex] u=R(r)*THETA(\vartheta)*\Phi(\phi)[/tex] and transform should i differentiate r^2 with respect to x?