# Time evolution of wave function in an infinite square well potential

• Apashanka
In summary, the infinite square well potential is a theoretical model in quantum mechanics that represents a particle confined to a one-dimensional space. The time evolution of a wave function in this potential is described by the Schrödinger equation and can be understood through the principle of superposition. The energy levels in the potential are quantized and determined by the size of the well, and the number of nodes in the wave function is directly related to the energy level.
Apashanka

## Homework Equations

For this question my ans. is coming option (3) since the time part of the wave comes out to be same for both the energy states which is (-1)^(-1/8) and (-1)^(-9/8) respectively (using exp(-iEt/ħ)).
But the correct option is given option (4).
Am I right??

## The Attempt at a Solution

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## What is the infinite square well potential?

The infinite square well potential is a theoretical model used in quantum mechanics to represent a particle confined to a one-dimensional space. It is characterized by a potential energy function that is infinitely high within a certain range and zero outside of that range.

## What is the time evolution of a wave function in an infinite square well potential?

The time evolution of a wave function in an infinite square well potential can be described by the Schrödinger equation, which is a fundamental equation in quantum mechanics. This equation allows us to calculate the probability density of finding a particle at a particular position and time in the well.

## How does the wave function evolve over time in an infinite square well potential?

The wave function in an infinite square well potential evolves over time according to the principle of superposition. This means that the initial wave function can be expressed as a linear combination of stationary states, each with a different energy. As time progresses, the amplitudes of these stationary states change, resulting in a changing wave function.

## What is the significance of the energy levels in an infinite square well potential?

The energy levels in an infinite square well potential represent the allowed energies of a particle confined to the well. These energy levels are quantized, meaning they can only take on discrete values, and are determined by the size of the well. The higher the energy level, the more energy the particle has and the more it can spread out within the well.

## How does the number of nodes in the wave function relate to the energy level in an infinite square well potential?

The number of nodes, or points where the wave function crosses the x-axis, in the wave function is directly related to the energy level in an infinite square well potential. The number of nodes is equal to the energy level minus one. This means that the higher the energy level, the more nodes there are in the wave function.

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