Calculate Eigen Function of 3D Potential Box w/ Doubled X Side

• SANKET HAQUE
In summary, an Eigen Function is a mathematical function that, when multiplied by a constant, returns the same function. It is calculated by writing out the Schrödinger equation and solving it for the potential box with a doubled X side using the separation of variables method and boundary conditions. A 3D Potential Box with Doubled X Side is a theoretical system used in quantum mechanics to study the behavior of confined particles. Calculating the Eigen Function of this system allows us to understand and predict its behavior and study properties such as energy levels. Additionally, the Eigen Function can be used to calculate other properties of the system, such as particle probability and average energy, due to its relationship to the wave function.
SANKET HAQUE
Suppose we have a 3D potential box having different length. Now suddenly we double the length of a particular side(Say along X direction) of the box. Can we calculate what will be the eigen function of the Hamiltonian. Is there Time Independent S.E. holds?

Yes you can do that but this sounds an awful lot like extremely standard QM HW problems so is this meant to be such?

1. What is an Eigen Function?

An Eigen Function is a mathematical function that, when multiplied by a constant, returns the same function. In other words, it is an input that produces an output that is proportional to the input itself.

2. How is an Eigen Function calculated?

In order to calculate the Eigen Function of a system, we must first write out the Schrödinger equation, which describes the behavior of quantum systems. We then solve this equation for the potential box with the doubled X side by using the separation of variables method and applying boundary conditions.

3. What is a 3D Potential Box with Doubled X Side?

A 3D Potential Box with Doubled X Side is a theoretical system used in quantum mechanics to study the behavior of particles confined within a box that has one side that is twice as long as the other two sides. This system is often used as a simplified model for real-life systems, such as atoms or molecules.

4. What is the significance of calculating the Eigen Function of a 3D Potential Box with Doubled X Side?

Calculating the Eigen Function of a 3D Potential Box with Doubled X Side allows us to understand and predict the behavior of particles within this system. It also helps us study the properties of quantum systems and their energy levels, which has applications in fields such as materials science and quantum computing.

5. Can the Eigen Function of a 3D Potential Box with Doubled X Side be used to calculate other properties of the system?

Yes, the Eigen Function can be used to calculate other properties of the system, such as the probability of finding a particle at a certain location or the average energy of the system. This is because the Eigen Function is related to the wave function, which contains all the information about the system's properties.

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