Solving Schroedinger's equation for Step Potential

Click For Summary
SUMMARY

This discussion focuses on solving Schrödinger's equation for a particle encountering a step potential, specifically where the potential energy V is zero for x<0 and V=Vo for x>0. The time-independent Schrödinger's equation is presented as -h²/2m d²ψ/dx² = Eψ for the first region and -h²/2m d²ψ/dx² = (Vo-E)ψ for the second region. A key point clarified is that while the potential energy and kinetic energy differ across regions, the total energy E remains constant due to the conservation of energy principle.

PREREQUISITES
  • Understanding of Schrödinger's equation
  • Familiarity with quantum mechanics concepts, particularly potential energy
  • Knowledge of conservation of energy principles
  • Basic calculus for differential equations
NEXT STEPS
  • Study the implications of potential energy in quantum mechanics
  • Learn about boundary conditions in quantum systems
  • Explore the concept of wave functions and their physical interpretations
  • Investigate the mathematical techniques for solving differential equations in quantum mechanics
USEFUL FOR

Students and professionals in physics, particularly those specializing in quantum mechanics, as well as anyone interested in understanding the behavior of particles in potential fields.

uday1236
Messages
3
Reaction score
0
Consider the case for a particle with energy E in a region where :
V = 0 , x<0; V=Vo, x>0;
for the first region when we write Schrödinger’s equation(Time independent) it will be
-h^2/2m d2ψ/dx2 = Eψ

and for second region it was
-h^2/2m d2ψ/dx2 = (Vo-E)ψ;


My doubt is that won't the Energy E be different in the second region because the particle experiences an impulse at x=0.

The case is where E<Vo.
 
Physics news on Phys.org
The potential energy U and the kinetic energy E - U are of course different in the two regions, but the total energy E is the same everywhere, by conservation of energy.
 
ok thanks...how could i forget E was total energy.
 

Similar threads

Undergrad Solving Schrodinger's eqn using ladder operators for potential V
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Derivations for Schrodinger's equations for potential step
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Is the Energy Expectation Value Always Real and Above a Minimum Potential?
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Potential step and tunneling effect
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Dimension of \lambda constant in \delta potential
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Question about the quantum harmonic oscillator
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Energies of bound state for delta function potential
  • · Replies 2 ·
Replies
2
Views
2K
Graduate 1D Quantum Well - Different width "naming" gives different result ?
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Solving Schrod. Eqn. for Potential Barrier with E > V
  • · Replies 5 ·
Replies
5
Views
2K
Graduate No solution with E=v0 for step potential
  • · Replies 2 ·
Replies
2
Views
2K