I need just ONE analytic solution to the time-dependent Schrodinger Equation.

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SUMMARY

The discussion centers on the quest for an analytic solution to the time-dependent Schrödinger Equation. The user expresses difficulty in finding such a solution, particularly for a general wave function, despite acknowledging existing solutions for specific cases like free particles and harmonic oscillators. The user aims to visualize the probability function over time but is uncertain if a general analytic solution exists without approximation.

PREREQUISITES
  • Understanding of the time-dependent Schrödinger Equation
  • Familiarity with wave functions and probability amplitudes
  • Knowledge of complex functions and their applications in quantum mechanics
  • Experience with specific solutions such as those for free particles and harmonic oscillators
NEXT STEPS
  • Research analytic solutions for the time-dependent Schrödinger Equation in various potential scenarios
  • Explore the mathematical techniques used to derive wave functions for quantum systems
  • Study the implications of approximations in quantum mechanics and their impact on wave function accuracy
  • Investigate numerical methods for visualizing probability functions over time
USEFUL FOR

Quantum physicists, students of quantum mechanics, and researchers seeking to understand or visualize solutions to the time-dependent Schrödinger Equation.

IronHamster
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I have been trying to find an analytic solution to the time-dependent Schrödinger Equation. I plan to make a movie of the probability function as it changes over time, but I can't seem to find any analytic solution for the wave function.

Is it possible to solve the time-dependent Schrödinger Equation without approximation, or should I stop looking?

If it would be helpful, I can show what methods I have tried so far.
 
Physics news on Phys.org
There are analytic solutions for either a free particle or for a harmonic oscillator with a wave function of the form exp[-a(t)x^2 - b(t)x], where a(t) and b(t) are particular complex functions of time.
 

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