Schrödinger to Statistics [Episode 1] - Free Quantum Particle Unbounded

Schrödinger to Statistics [Episode 1] - Free Quantum Particle Unbounded.

So this is the first episode of the new series. In it we will solve the Schrödinger Equation for some particular system, whatever that may be, and then use the energy eigenvalues to obtain the average energy via Statistical Mechanics.

In this case, we are solving for a 1D, singular, unbounded, free particle (i.e. V(x)=0). As we can see, all the Quantum Mechanical effects will be lost since there are no boundary conditions to quantise the wave function thus we will have a continuous spectrum of Eigenvalues for the energy. Hence, this will give rise to a classical result, however this is where the similarities will end. Tune in for next episode to learn all about it :)

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