Question

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• $\sf Explain \:Schrodinger's \:Wave\: Equation$
• $\sf also \:explain,\: What \:does$ " $d$ " $\sf represent \:in$ " $d \psi^{2}$

50 points!
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Answer 1

For understanding this equation You should learn cylinderical co - ordinate system
basically it tells the probability of finding an electron around the nucleus
in cylinderical co ordinate system when we fix sin thita and cos thita we get a definite direction and then rotate that dirn 360°and we get probability at that dirn
the symbol is deva ziee which is used to solve the function
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Answer 2

$<b><big>Answer</b></big>$

At the beginning of the twentieth century, experimental evidence suggested that atomic particles were also wave-like in nature. For example, electrons were found to give diffraction patterns when passed through a double slit in a similar way to light waves. Therefore, it was reasonable to assume that a wave equation could explain the behaviour of atomic particles. 

Schrodinger was the first person to write down such a wave equation. Much discussion then centred on what the equation meant. The eigenvalues of the wave equation were shown to be equal to the energy levels of the quantum mechanical system, and the best test of the equation was when it was used to solve for the energy levels of the Hydrogen atom, and the energy levels were found to be in accord with Rydberg's Law. 

It was initially much less obvious what the wavefunction of the equation was. After much debate, the wavefunction is now accepted to be a probability distribution. The Schrodinger equation is used to find the allowed energy levels of quantum mechanical systems (such as atoms, or transistors). The associated wavefunction gives the probability of finding the particle at a certain position.
Answered by: Ian Taylor, Ph.D., Theoretical Physics (Cambridge), PhD (Durham), UK.

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