Identifying number of node of an arbitrary wave function Given an arbitrary wave function, what is the most general way to identify number of its nodes? By arbitrary, I mean we don't have any predefined conditions (like wave function of an atom, a harmonic oscillator, a particle in a box or etc).
 A: *I've decided to come back and edit this answer to clarify it somewhat. Originally, when I wrote it, I did not realize there was a superfluous point, so I thought I would remove it and improve the readability.
A node occurs anytime the wave function is zero. Nodes correspond to points of zero probability. However, the probability (say for the position) of any "point" is zero, because the wavefunction is understood to be a probability distribution function (PDF), and as such, it is usually integrated over a finite, positive domain, when calculating probabilities.
Therefore, you simply need to equate the wavefunction to zero and solve it:
$\psi(x)=0$
As you may know, in simple cases, such as a particle trapped in an infinite potential (particle in a box), you end up having to equate spatial wavefunctions of a trigonometric form (i.e. sines or cosines, depending on whether the principal quantum number is even or odd) to zero. In such cases, you obtain nodes at integer, or fractional, multiples of $\pi$ over the domain, again, depending on the spatial form of the wavefunction. For the ground state, the only nodes to occur are at the walls, with the total number of nodes in each eigenstate equal to $\ n + 1$, where $\ n $ is the principal quantum number ($\ n\ge1$).
In more complex cases, analytic (exact) solutions may not necessarily exist, and as such, numerical approximations will be required. Here, a computer can help.
