Probability density doesn't oscillate with time

Broken]In summary, the probability density of a stationary state does not oscillate with time, as it is the "square" of the wavefunction which remains constant due to the multiplication of e-iEt with its complex conjugate. However, the wavefunction itself does evolve in time according to ψ(x,t)=f(x)e-iEt. The reason for this is because the probability density is a superposition of several eigenfunctions. For a general state, the probability density does vary with time. Additional information and animations can be found at the provided links.
  • #1
solas99
69
1
why the probability density doesn't oscillate with time?
 
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  • #2
It can do - and usually does, for instance, in a stationary state.
What is the situation.
 
  • #3
For a stationary state the probability density does not oscillate in time.

The wavefunction of a stationary state does evolve in time according to ψ(x,t)=f(x)e-iEt, where f(x) is an eigenfunction of the Hamiltonian, and E is the corresponding eigenvalue. However, the probability density is the "square" of the wavefunction, ψψ*, where the multiplication of e-iEt with the complex conjugatate of eiEt gives e0=1, which doesn't change with time.

The probability density of a general state does evolve in time, because it is the superposition of several eigenfunctions.
 
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  • #4
Oh I get you - I misread.
Yeah - the probability density of a stationary state does not vary with time, which is sort-of why it is a stationary state.
Still need more info to answer OPs question properly.
 
  • #5
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FAQ: Probability density doesn't oscillate with time

What does it mean for probability density to not oscillate with time?

When we say that probability density does not oscillate with time, we mean that the likelihood of a particular event occurring does not change over time. In other words, the probability of an event happening at a specific time remains constant.

Why is it important for probability density to not oscillate with time?

Having a constant probability density allows us to make accurate predictions about the likelihood of events occurring. It also allows us to study the behavior of systems over time and make meaningful comparisons.

3. What factors can cause probability density to oscillate with time?

Probability density can oscillate with time due to external influences or internal dynamics within a system. These can include changes in environmental conditions, interactions with other systems, or fluctuations in the system itself.

4. Is it possible for probability density to oscillate with time in certain situations?

Yes, it is possible for probability density to oscillate with time in certain situations. For example, in systems that exhibit chaotic behavior, the probability of a certain event occurring can vary over time in an unpredictable manner.

5. How do scientists study the behavior of probability density over time?

Scientists use mathematical models and statistical analysis to study the behavior of probability density over time. They can also conduct experiments and collect data to observe how probability density changes in different scenarios.

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