Definition of stationary state (for wave function quantum)

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SUMMARY

The discussion clarifies that a stationary state in quantum mechanics is represented by the time-independent wave function, expressed as Ψ(x,y,z,t) = ψ(x,y,z)e^{-iEt/ℏ}. This formulation indicates that the wave function maintains a constant probability density over time, akin to a standing wave. The distinction between stationary states and time-dependent states is emphasized, with stationary states being characterized by their time-invariant properties.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with wave functions and their mathematical representations
  • Knowledge of the Planck constant (ℏ) and energy (E) in quantum contexts
  • Basic grasp of the concept of standing waves
NEXT STEPS
  • Study the implications of the Schrödinger equation in stationary states
  • Explore the concept of probability density in quantum mechanics
  • Learn about the differences between time-dependent and time-independent wave functions
  • Investigate applications of stationary states in quantum systems
USEFUL FOR

Students of quantum mechanics, physicists, and anyone interested in the mathematical foundations of wave functions and their applications in quantum theory.

AStaunton
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Hi there

My textbook says the following is the time independent wave function for a stationary state:

[tex]\Psi(x,y,z,t)=\psi(x,y,z)e^{-iEt/\bar{h}}[/tex]

Just trying to get my definitions straight...is a stationary state the analogue of a standing wave?
 
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correction****

time dependent
 

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