Basic Question about Time Dependent Wave Functions

In summary, a time dependent wave function is a mathematical representation of the possible states of a quantum system at different points in time, taking into account the changes in the system. It is different from a time independent wave function, which does not consider time changes. The Schrödinger equation is a fundamental equation in quantum mechanics that relates to time dependent wave functions, allowing us to calculate the wave function at any point in time. While time dependent wave functions can be used for all quantum systems, simpler systems may use time independent wave functions instead. The time dependence of a wave function can be observed through experiments such as the double-slit experiment or the Stern-Gerlach experiment.
  • #1
atomicpedals
209
7
The situation I have in my problem is the standard infinite square well from 0 to L. The normalized eigenfunction is

[itex]\phi[/itex]n(x) = [itex]\sqrt{2/L}[/itex]sin(n[itex]\pi[/itex]x/L) for n=1,2,3,...

if my wave function at time t=0 is then

cos(a)[itex]\phi[/itex]1(x)+sin(a)[itex]\phi[/itex]2(x)

is my wave function at more general time t something like

(cos(a)[itex]\phi[/itex]1(x))*exp(iEt/[itex]\hbar[/itex])+(sin(a)[itex]\phi[/itex]2(x))*exp(iEt/[itex]\hbar[/itex]) ?
 
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  • #2
Yes, it's something like that, but the E's for the two terms are different.
 
  • #3
Right, E is dependent on n.
 

What is a time dependent wave function?

A time dependent wave function is a mathematical representation of the possible states of a quantum system at different points in time. It describes the probability of finding a particle at a particular location at a specific time.

How is a time dependent wave function different from a time independent wave function?

A time dependent wave function takes into account the changes in a quantum system over time, while a time independent wave function does not. A time dependent wave function is necessary for studying systems that are not in a stationary state.

What is the Schrödinger equation and how does it relate to time dependent wave functions?

The Schrödinger equation is a fundamental equation in quantum mechanics that describes the evolution of a quantum state over time. It is a key component in understanding time dependent wave functions, as it allows us to calculate the wave function at any point in time.

Can time dependent wave functions be used for all quantum systems?

Yes, time dependent wave functions can be used for any quantum system, regardless of its complexity. However, for simpler systems with fewer particles, time independent wave functions may be more appropriate.

How is the time dependence of a wave function experimentally observed?

The time dependence of a wave function can be observed through experiments such as the double-slit experiment or the Stern-Gerlach experiment. These experiments involve measuring the probability of a particle's position at different points in time, which is described by the time dependent wave function.

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