##### Asked by: Yokasta Bilhau

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**

- Start at x = 0 m and ψ = 0 (also I will pick ψ-dot equal to zero).
- Use Schrödinger's equation to calculate ψ-double dot.
- Use ψ-double dot to calculate ψ-dot.
- Use ψ-dot to calculate ψ.
- 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.