Separating Schrodinger's Equation

Thread starter MiCasilla
Start date Aug 17, 2003
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Schrodinger's equation

In summary, Schrodinger's equation is a fundamental formula in quantum mechanics that describes how a particle's wave function changes over time. It is derived from the principles of energy conservation and wave-particle duality, and can be separated into two parts: the time-independent and time-dependent equations. The former determines the energy levels and stationary states of a system, while the latter describes the evolution of these states over time. This separation allows for a more efficient and simplified approach to solving the equation, making it a crucial tool in understanding the behavior of quantum systems.

Aug 17, 2003

MiCasilla

I'm looking for the mathematical demonstration that the Time Dependent Schrodinger Equation can be separated into time-independent Schrodinger equation and time evolution equation.

Does anybody know a link which such demonstration?

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Aug 17, 2003

futz

https://www.physicsforums.com/showthread.php?s=&threadid=4860

Posting in one forum is probably sufficient...

1. What is Schrodinger's Equation?

Schrodinger's Equation is a mathematical formula used in quantum mechanics to describe the behavior of a quantum system over time. It is named after physicist Erwin Schrodinger who first proposed it in 1926.

2. How is Schrodinger's Equation used to separate a quantum system?

Schrodinger's Equation can be used to analyze the wave function of a quantum system and determine the probability of the system existing in a particular state. This allows for the separation of the system into distinct energy levels or states.

3. What is the significance of separating Schrodinger's Equation?

The separation of Schrodinger's Equation allows for a better understanding of the behavior of quantum systems, as well as the prediction of their future states. It also plays a crucial role in the development of quantum technologies and applications.

4. What are some techniques used to separate Schrodinger's Equation?

There are several techniques used to separate Schrodinger's Equation, including the method of separation of variables, the Fourier transform, and the use of ladder operators. These techniques help to simplify the equation and make it easier to solve.

5. Can Schrodinger's Equation be applied to all quantum systems?

While Schrodinger's Equation is a fundamental tool in quantum mechanics, it is not applicable to all quantum systems. Some systems, such as those with time-dependent potentials or interactions, require more complex equations to accurately describe their behavior.