Consider the motion of a quantum particle in a potential V(x)-ax. Use the WKB approximation to determine how the energy of the bound state E, varies with n and a for large values of n.

In quantum mechanics, the motion of a particle in a potential V(x)=axV(x) = ax, where aa is a constant, can be analyzed using the WKB approximation, particularly for the case of bound states. The WKB (Wentzel–Kramers–Brillouin) approximation is a semiclassical method used to find approximate solutions to the Schrödinger equation when the potential varies slowly. It involves solving the Schrödinger equation in regions where the classical action is large.

The Schrödinger equation for a particle of mass mm moving in the potential V(x)=axV(x) = ax is given by:

−ℏ22md2ψ(x)dx2+axψ(x)=Eψ(x)-\frac{\hbar^2}{2m} \frac{d^2 \psi(x)}{dx^2} + ax __________ _____ ______ ________ ______.
_____ _____ __________ ____ ________ _____ ________.
______ ______ ______ _____ ________ ______ _______ ____.
_____ ______ _________ __________ _____ __________ _________ _____ _______.
__________ ______ ____ ___ ______ _________ ________ ___ _______ _____ _________ ____.
____ ___ __________ _____ __________ _____ ________ ______ _______ ______.
_____ _______ ___ _______ __________.
_______ _________ ___ ___ _______ _________ ___ ___ __________ __________ ___ ________.
___ _______ ____ ____ _________ _____.
______ ____ ___ _________ _________ ___ ____ _______ __________.
___ _________ ___ ___ ________.
______ __________ __________ _________ _________ ______ ______.
________ ______ ________ ___ ____ _________ __________ _____ ___ ______ __________ __________.
____ _____ ____ ____ ____ ______ ________ __________.
_____ _________ _____ _____ _________ ____ ______ __________ ________ ________ ___ __________.
___ ___ __________ ________ ______ _________ __________ __________ _______ ______ ______.
_______ _______ ________ _______ _________ _______.
__________ _________ ___ ______ __________ ________ ___ ____.
______ _______ __________ ___ _____ __________ ________ ____.
_______ ______ ______ ______ __________ _______ ______ ______ _____ ____ ____.
_______ ___ __________ ___ ____ _______ ________ ___ ____ ____ _____ ___.
___ _________ ___ ___ _______.
______ ___ _______ _________ _______ _______ ________ __________ __________ ____.
__________ ____ ________ _____ _____ _____ _________ ____ ____.
__________ __________ ________ _________ __________ _________ _____ ___ ____ __________ __________ ___.
_______ _______ ___ ________ ____ __________ ________ _________.
__________ __________ ___ ___ _______ _______ _______ _______.
____ ______ ________ _________ ____ __________ ______.
__________ _____ ___ _____ ____.
__________ ____ ___ ___ _______ _______ ___ __________.
__________ ____ _________ _______ _______.
_______ ______ ______ ___ ______ ______ ________.
_______ __________ ________ _________ _______ ______ _____.
______ ________ _____ _________ _____ ___ ____ _________ __________ ________ ________ _______.
___ _____ _______ ________ __________ ____.
__________ ________ ___ _______ _______ ________ _____ __________.
___ ______ _____ ____ ____ _____ ________ ________ ___ _________ ________.
________ __________ __________ _______ ________ ___ _____.
__________ _____ _______ __________ ________ ______.
___ _________ ________ _______ ___ ____.
_________ _________ ______ _______ _____ __________ ________ _____ ______.
________ _____ _____ __________ _____ __________ _____ _____.
_________ _____ _________ ___ _____ __________ ______ _______ __________ _____.
____ ____ ________ ____ ___ ________.
________ _______ ___ _______ ___ __________ _________ ____ _____.
Get Full Answer on WhatsApp