What's in the schrodinger wave equation?

[Saitama]

I have just completed Atomic Structure from my textbook. In that a Schrödinger Wave Equation is mentioned and after that it is written that it is not in the scope of this book to solve this equation. I want to know what is so hard in the Schrödinger wave equation that it is not of my level?

 

[czelaya]

I wondered the same thing also when I took high school chemistry and, again, in college when I took introductory physics course.

The reason why these books state this is because the Schrödinger Equation is a partial differential equation.Thus it takes several semesters of calculus, multivariable calculus, linear algebra, differential equations, and partial differential equations. Then as you take quantum mechanics and learn about the Schrödinger equation you're exposed to even more mathematics (spherical coordinates, group theory, Hermite polynomials, and so forth).

In addition, a number of physics courses are very helpful in understanding the derivation of the Schrödinger equation itself(especially classical mechanics).

In other words, if you saw the equation it wouldn't make that much sense understanding it mathematically. Also the equation takes on many different forms according to the system it is defining.

However, there are books that discuss the nature and give you a great flavor of what the Schrödinger Equation encapsulates (Quantum: A Guide For The Perplexed Jim Al-Khalili).

 

[Saitama]

I wondered the same thing also when I took high school chemistry and, again, in college when I took introductory physics course.

The reason why these books state this is because the Schrödinger Equation is a partial differential equation.Thus it takes several semesters of calculus, multivariable calculus, linear algebra, differential equations, and partial differential equations. Then as you take quantum mechanics and learn about the Schrödinger equation you're exposed to even more mathematics (spherical coordinates, group theory, Hermite polynomials, and so forth).

In addition, a number of physics courses are very helpful in understanding the derivation of the Schrödinger equation itself(especially classical mechanics).

In other words, if you saw the equation it wouldn't make that much sense understanding it mathematically. Also the equation takes on many different forms according to the system it is defining.

However, there are books that discuss the nature and give you a great flavor of what the Schrödinger Equation encapsulates (Quantum: A Guide For The Perplexed Jim Al-Khalili).

That seems to be a lot of mathematics. I think i should not go there .

There was a question once asked by my teacher on the Schrödinger wave equation. The Schrödinger wave question for hydrogen atom was given and we were asked to find out the minimum and maximum radial distance of node from the nucleus. We were able to solve it.
But in my class, there's an extra-ordinary student, teacher asked her that which orbital does this Schrödinger wave equation represents and she was not able to answer it? But i am interested to know how we can determine which orbital does the equation represent. Here's the equation which was given in the question:-

$$\psi(radial)=\frac{1}{16\sqrt{4}}(\frac{Z}{a_0})^{\frac{3}{2}}[(\sigma-1)(\sigma^2-8\sigma+12)]e^{\frac{-\sigma}{2}}$$

where a₀ and Z are constants in which the answer can be expressed and $\sigma=\frac{2Zr}{a_0}$.