Infinitesimal propagator

Thread starter Dr.Maurice
Start date May 4, 2015
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Infinitesimal Propagator

In summary, an infinitesimal propagator is a mathematical tool used in quantum mechanics to describe the time evolution of a quantum system in small time intervals. It differs from a finite propagator in that it approximates the continuous time evolution and is used to calculate the probability amplitude for a particle to move from one point in space to another. The formula for an infinitesimal propagator is based on the time-dependent Schrödinger equation. However, it has limitations in accurately predicting behavior over longer time periods and assumes a continuous time evolution.

May 4, 2015

Dr.Maurice

How does the wavefunction propagate for infinitesimal times? Please no Feynman path integral arguments!

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May 4, 2015

Dr.Maurice

The midpoint rules are false (Makri, Miller, me)

May 4, 2015

rumborak

I may be misunderstanding the question, but are you asking the QM version of Zeno's paradox?

1. What is an infinitesimal propagator?

An infinitesimal propagator is a mathematical tool used in quantum mechanics to describe the time evolution of a quantum system. It represents the probability amplitude for a particle to move from one point in space to another in a small time interval.

2. How does an infinitesimal propagator differ from a finite propagator?

An infinitesimal propagator considers the time evolution of a quantum system in small time intervals, while a finite propagator considers the time evolution over a larger time interval. Infinitesimal propagators are often used to approximate the effects of a continuous time evolution.

3. What is the formula for an infinitesimal propagator?

The formula for an infinitesimal propagator is given by the time-dependent Schrödinger equation:
$\Large i\hbar\frac{\partial}{\partial{t}}\psi(x,t)=\hat{H}\psi(x,t)$

4. How is an infinitesimal propagator used in quantum mechanics?

An infinitesimal propagator is used to calculate the probability amplitude for a particle to move from one point in space to another in a small time interval. This is important in understanding the time evolution of quantum systems and predicting the behavior of particles at different points in time.

5. Are there any limitations to using an infinitesimal propagator?

Yes, there are limitations to using an infinitesimal propagator. It is only valid for small time intervals and cannot accurately predict the behavior of particles over longer time periods. Additionally, it is based on the assumption of a continuous time evolution, which may not always hold true in quantum systems.