**Required math: calculus **

**Required physics: **Schrödinger equation

Reference: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 2.7.

As another example of an explicit case of a particle in the infinite square well, we can consider a particle that starts off with a triangular wave function, of form

We find from normalization:

so

The general solution is a linear combination of the stationary states:

and at , we get

To find we need the coefficients which we get from the orthonormality of the stationary states:

Doing the integral (by hand or use Maple) gives:

The probability that the energy is is . (Incidentally, since we know that , we get for free that .)

The average energy can be found by using the energy levels for the infinite square well: we have, using the formula

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Atta UllahPlease, Can u briefly explain that how u got the Value of A.

gwrowePost authorIt comes from normalizing the wave function. Just insert eqn 1 into eqn 2 and integrate.