asked in category: General Last Updated: 15th April, 2020

# How do you solve a particle in a box problem?

Numerical Solution for a Particle in a Box
1. Start at x = 0 m and ψ = 0 (also I will pick ψ-dot equal to zero).
2. Use Schrödinger's equation to calculate ψ-double dot.
3. Use ψ-double dot to calculate ψ-dot.
4. Use ψ-dot to calculate ψ.
5. Update the x-position and do it again until you get to the end of the box.

Besides, what is particle in a box used for?

Because of its mathematical simplicity, the particle in a box model is used to find approximate solutions for more complex physical systems in which a particle is trapped in a narrow region of low electric potential between two high potential barriers.

Beside above, what is zero point energy of a particle in one dimensional box? The energy of a particle is quantized and. The lowest possible energy of a particle is NOT zero. This is called the zero-point energy and means the particle can never be at rest because it always has some kinetic energy.

Consequently, what is the minimum energy possessed by the particle in a box?

Explanation: The minimum energy possessed by a particle inside a box with infinitely hard walls is equal to frac{pi^2hbar^2}{2mL^2}. The particle can never be at rest, as it will violate Heisenberg's Uncertainty Principle.

Why potential energy is zero inside the box?

So, the particle inside the box experiences zero potential inside and it can not come out of the box as the potential outside of it is infinite. Again, as it is one dimensional, so the particle is only capable to move in one dimension,i.e. it has only one degree of freedom. It is also known as infinite potential well.

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15th April, 2020

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