Probability of finding a particle in a 1-D box max. at centre?

I
Thread starter Apashanka
Start date May 27, 2020
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Box Max Particle Probability

In summary, the probability of finding a particle at the center of a 1-D box is determined by the quantum state and is given by the square of the wave function. The maximum probability does not change with the size of the box due to the symmetry of the wave function. The probability can never be zero as the wave function is continuous and non-zero at the center. The maximum probability is directly proportional to the energy level of the particle. The distribution of probabilities follows a bell-shaped curve, with the highest probability at the center and decreasing probabilities towards the edges of the box. This is due to the wave function having a higher amplitude at the center and lower amplitudes towards the edges.

May 27, 2020

Apashanka

TL;DR Summary: Probability density ##(2/L)*sin^2(\pi x/L)##

From the probability density plot why it is max at the centre of the box...e.g probability to find the particle per unit le gth is max. at the centre of the box??why not at any other position??

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May 27, 2020

anuttarasammyak

Gold Member

You say about the ground state n=1. As for excited states for larger n you will see almost homogeneous distribution as you may expect.

Related to Probability of finding a particle in a 1-D box max. at centre?

1. What is the probability of finding a particle in the center of a 1-D box?

The probability of finding a particle in the center of a 1-D box is dependent on the length of the box and the energy level of the particle. In general, the probability is higher for shorter boxes and lower for longer boxes.

2. How is the probability of finding a particle in the center of a 1-D box calculated?

The probability is calculated using the Schrödinger equation and the wave function of the particle in the box. The square of the wave function at the center of the box gives the probability of finding the particle at that point.

3. Does the probability of finding a particle in the center of a 1-D box change over time?

Yes, the probability of finding a particle in the center of a 1-D box can change over time. This is because the wave function of the particle can evolve and change shape, affecting the probability distribution throughout the box.

4. How does the potential energy of the particle affect the probability of finding it in the center of a 1-D box?

The potential energy of the particle affects the probability of finding it in the center of a 1-D box by influencing the shape and amplitude of the wave function. Higher potential energy levels can lead to a lower probability of finding the particle in the center of the box.

5. Can the probability of finding a particle in the center of a 1-D box be greater than 1?

No, the probability of finding a particle in the center of a 1-D box cannot be greater than 1. This is because the probability is a measure of the likelihood of finding the particle at a specific point, and a probability greater than 1 would imply a certainty of finding the particle at that point.