Undergrad One-Dimensional System: Boundary Condition Applicability

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SUMMARY

The discussion focuses on the applicability of the boundary condition that the derivative of the wave function Ψ(x) must be continuous at every point in one-dimensional systems. This condition holds true when the potential energy V(x) is finite throughout the domain. Notable counterexamples include the particle in a box scenario and the delta function potential, where this continuity condition does not apply.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with wave functions and their properties
  • Knowledge of potential energy functions in quantum systems
  • Concept of boundary conditions in differential equations
NEXT STEPS
  • Research the implications of finite potential energy in quantum mechanics
  • Study the particle in a box model and its boundary conditions
  • Examine the delta function potential and its effects on wave functions
  • Explore advanced topics in quantum mechanics related to boundary value problems
USEFUL FOR

Students and professionals in physics, particularly those specializing in quantum mechanics, as well as researchers focusing on wave function behavior and boundary conditions in one-dimensional systems.

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In one dimensional system the boundary condition that the derivative of the wave function Ψ(x) should be continuous at every point is applicable whenever?
 
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GANTI_RAVITEJA said:
In one dimensional system the boundary condition that the derivative of the wave function Ψ(x) should be continuous at every point is applicable whenever?

It's applicable when the potential energy V(x) is finite everywhere. Counterexamples include the particle in a box and the delta function potential.
 
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Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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