In this article, we outlined the necessary steps in calculating the radial wavefunctions for the Hydrogen atom. Thus, the radial wavefunctions particularly , and are easily obtained  without bothering to normalize it.

We use the formula below to find the wavefunction,

                               ( 1)

where

                                        (2)

while is determined by the recursion formula given by,

                         (3)

and

                                                           (4)

(i) Now, finding

Using equation 1, we need to solve first the coefficient from (eqn. 3), with and .

Knowing the value of , (eqn. 2) can now be easily determined,

                        (5)

Substituting the value of the calculated coefficients to (eqn. 5), we then have

                                        (6)

Thus,

             (7)

Plugging in (eqn. 4) to (eqn. 7), we finally have

Following the same process in (i), the rest of the wavefunctions are just straightforward.

(ii) For

Determining first the coefficients, with and ,

Then,

.

Thus,

(iii) We have the coefficients for with and ,

Using again (eqn. 1), we have

We finally generated the radial wavefunctions (, , ) for the hydrogen atom which is the main aim of this paper.

These students have previously studied about a year or more of quantum concepts through formal classes in modern physics and quantum mechanics with different instructors.

In a 10-minute short exercise, they wrote questions they have about the concept of wavefunction in quantum mechanics. Some of the more common questions are the subject of this post.

Why is it called the wavefunction? Why is it important in quantum mechanics?

The wavefunction describes the state of the system completely. Is the wavefunction an observable? If not, what’s the sense of showing a graphical representation of it?

How important is the wavefunction in the real world? How was it created without knowing its physical interpretation?

Is there another way of obtaining the wavefunction apart from solving Schrodinger equation?

How do we know or prove that the wavefunction obtained from a system is true and correct?

Are there classical and quantum properties of ?

What is the difference if the wavefunction is expressed as or ? How to separate the time-independent part?

What does it mean that is square-integrable? What is the physical meaning of the norm of ?

What is the significance of in Hilbert’s space?

Is probability the only meaning that can be attached to ?

These are just a few of the lingering questions students would have about learning the basic concepts of quantum mechanics. These questions show the many interesting aspects of quantum mechanics; in part showing its reputation as a tough course to master for young students.