Solve 1-D Potential Barrier: Electron, Width 8 Angstroms, Depth 12eV

[rajasekhar_09]

HI,all

This is rajasekhar ,
Please guide me how to solve below problem.

An electron moves in a one-dimensional potential of width 8 angstroms and depth 12eV then how to found number of bound states present?


Thanks&Regaurds

 

[xepma]

Start with solving (or looking up) the solution for the 1D potential well -- you can find the treatment in any introductory book on Quantum Mechanics. What are the bound states for such a system? How many are there? You'll need to relate these abstract answers to the numbers you mentioned.

 

[Entropia]

,
Rajasekhar

Hello Rajasekhar,

To solve this problem, we can use the Schrödinger equation to determine the energy levels and the number of bound states of the electron in the potential barrier. The Schrödinger equation is a fundamental equation in quantum mechanics that describes the behavior of particles in a potential.

To solve the Schrödinger equation for this problem, we need to first determine the potential function for the one-dimensional barrier. In this case, the potential function can be written as V(x) = 12eV for x < 0 and x > 8 angstroms, and V(x) = 0 for 0 < x < 8 angstroms.

We can then use the Schrödinger equation to find the energy levels and wavefunctions of the electron in this potential. The energy levels will correspond to the bound states of the electron, while the wavefunctions will show the spatial distribution of the electron within the barrier.

Once we have the energy levels, we can determine the number of bound states by counting the number of energy levels that are below the barrier height of 12eV. These energy levels represent the bound states of the electron within the barrier.

I hope this helps guide you in solving the problem. If you need further assistance, you can consult a textbook or seek help from a colleague or professor. Good luck!