What is a value of psi* for a particle in 1D box stationary state?

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Discussion Overview

The discussion revolves around the definition and calculation of the complex conjugate of the wave function, psi (ψ), for a particle in a one-dimensional box stationary state. Participants explore the mathematical representation and implications of psi and its complex conjugate, psi*.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant states that psi is equal to (2/a)^(1/2) sin(n π x/a) and asks for the value of psi*.
  • Another participant explains that the complex conjugate of psi is identical to psi in this case.
  • A participant seeks clarification on the definition of psi* and what the asterisk signifies.
  • One participant provides the time-dependent form of the wave function and shows how to derive the complex conjugate by changing i to -i.
  • Another participant suggests that the original question may not have intended to include time dependence, indicating a possible misunderstanding.

Areas of Agreement / Disagreement

There is some agreement on the definition of psi and its complex conjugate, but there is also uncertainty regarding the inclusion of time dependence in the discussion. The original intent of the question remains unclear.

Contextual Notes

The discussion does not resolve the ambiguity regarding the inclusion of time dependence in the wave function and its implications for the complex conjugate.

ohhhnooo
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I know that psi is equal to (2/a)^1/2 sin(n pi x/a)? what is psi*?
 
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Complex conjugate of "psi"...In your case,it's identical to "psi"...

Daniel.
 
ohhhnooo said:
I know that psi is equal to (2/a)^1/2 sin(n pi x/a)? what is psi*?

How is [itex]\psi^*[/itex] defined ? Or simpler still, what does the * do ?
 
ohhhnooo said:
I know that psi is equal to (2/a)^1/2 sin(n pi x/a)? what is psi*?

Actually, including the time dependence, it's

[tex]\Psi(x,t) = \sqrt {\frac {2} {a}} \sin \left (n \pi \frac {x} {a} \right ) \exp \left (-i \frac {E_n} {\hbar} t \right )[/tex]

so the complex conjugate is

[tex]\Psi^*(x,t) = \sqrt {\frac {2} {a}} \sin \left (n \pi \frac {x} {a} \right ) \exp \left (i \frac {E_n} {\hbar} t \right )[/tex]

The complex conjugate means simply, change i to -i (and -i to i) everywhere.
 
Last edited:
In that case,he (probably) would have spelled "Psi"...He didn't intend to include the time dependence...

Daniel.
 

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