In my textbook it is given that
'The wave function describes the position and state of the electron and its square gives the probability density of electrons.'
Can someone give me a very simple example of a wave function with explanation? (Note: This question is not a duplicate. I have searched for other questions of this type but the answers were overwhelmingly difficult to understand.)
Answer
A wave function is a complex-valued function $f$ defined on ${\mathbb R}^1$ (if your electron is confined to a line) or on ${\mathbb R}^2$ (if your electron is confined to a plane) or ${\mathbb R}^3$ (if your electron ranges over three-space), and satisfying $$\int |f|^2=1$$ (where the integral is defined over the entire line or plane or 3-space).
Every electron has an associated wave function, and any function satisfying the above can be the wave function associated to some electron.
The wave function tells you everything there is to know about the electron. For example, if $A$ is any set, and if you perform an experiment that answers the question "is the electron in the set $A$?", then the probability you'll get a "yes" answer is given by $$\int_A |f|^2$$
(So in particular, if $A$ is the entire space, you're asking "Is the electron anywhere at all?", and the probability of a yes answer is $1$.)
The next steps are to learn:
1) How do I use this wave function to predict the outcomes of questions about something other than the electron's location, such as, for example, its momentum?
and
2) How does this wave function change over time?
I don't think you're quite yet at the point of addressing those questions (though you will be soon enough).
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