What is the advantage of squaring the wave function and then plotting against distance from the nucleus?
Answers
Answer:Squared gets rid of the negatives values (up versus down). It becomes the distance from the zero location. Some great work by Hilbert proved that given lots
Explanation:
Answer:
A wave function in quantum mechanics is a description of the quantum state of a system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. .The state of such a particle is completely described by its wave function Ψ(x,t). So it’s the Solutions of Schrodinger Equation
and The solution is Ψ(x,t) where x is position and t is time. This is a complex-valued function of two real variables x and t. Following are the general forms of the wave function for systems in higher dimensions and more particles, as well as including other degrees of freedom than position coordinates or momentum components.
Since Ψ(x,t) is analogous to Amplitude of wave.
So for any kind of wave, we know I is directly proportional to A^2. The same is also for Quantum Mechanics .Here the Intensity means frequently observing the particle in a particular place in other words, Probability of finding the particle in a particular place .
Therefore chance or probability of finding the particle in place is obtained by |Ψ(x)|^2 = Ψ(x)Ψ(x)* which is Probability Amplitude Function.
Here given a graphical representation of Ψ(x) & Ψ(x)|^2 for an electron bounded in different orbits in an atom to visualize the fact