What does show solutions to the schroedinger eqn mean?

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In summary, the conversation discussed the meaning of "show solutions to the schroedinger eqn" and the process of proving that a given wave function is a solution to the Schrodinger Equation. It was mentioned that this may involve finding and accounting for negligible parts of the wave function. The main goal is to ensure that the Schrodinger Equation holds true when the wave function is plugged in.
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What does "show solutions to the schroedinger eqn" mean?

I'm sorry for the very beginner question, I'm a mature student who's just come back to University so I'm unaccustomed to the terminology.

The question has given us a wave function and asked us to show that at later times Ψ is a solution to the schroedinger equation.

Is all I need to do plug it in and show that LHS = RHS?
 
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If they ask specifically for [itex]\psi[/itex] at later times then I'm guessing you may want to find the parts of [itex]\psi[/itex] that become negligible for large t. Then plugging in it should work.
 
  • #3


You're right. Write down the initial state, and then the time-dependent wave function, plug it into the Schrodinger Equation, it make sure it holds identically.
 

Related to What does show solutions to the schroedinger eqn mean?

1. What is the Schrödinger equation?

The Schrödinger equation is a mathematical equation that describes how the quantum state of a physical system changes with time. It is a fundamental equation in quantum mechanics and is used to calculate the probability of finding a particle at a certain position in space and time.

2. How does the Schrödinger equation relate to quantum mechanics?

The Schrödinger equation is the central equation of quantum mechanics. It describes the behavior of particles on a microscopic scale, where classical mechanics fails to accurately predict their movements. The solutions to the Schrödinger equation provide information about the possible locations and energies of particles.

3. What does it mean to show solutions to the Schrödinger equation?

Showcasing solutions to the Schrödinger equation means presenting the possible outcomes for a particle's position and energy based on the mathematical equation. These solutions are typically in the form of wavefunctions, which represent the probability of finding a particle at a certain location.

4. How are solutions to the Schrödinger equation used in research?

Solutions to the Schrödinger equation are used extensively in research to understand the behavior of particles on a quantum level. They are used to calculate the properties of atoms, molecules, and other quantum systems, and to make predictions about their behavior and interactions.

5. Are the solutions to the Schrödinger equation always accurate?

The solutions to the Schrödinger equation are accurate within the framework of quantum mechanics. However, they are not always a perfect representation of reality, as they are based on probabilities and cannot predict the exact outcome of a particle's behavior. Additionally, the accuracy of the solutions can be affected by external factors such as measurement errors or the presence of other particles.

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