ψ And ψ2 significance

ψ And ψ2 significance

• 1.
  Significance of ψand ψ2 Dr. Mithil Fal Desai Shree Mallikarjun and Shri Chetan Manju Desai College Canacona Goa ψ ψ2
• 2.
  Ψ and Ψ2 Ψ(Psi) is a wave function represented in the Schrodinger wave equation, which represents the state of the electron. Its corresponding probability density (Ψ2) gives the probability of finding the electron in a particular region in space.
• 3.
  Schrodinger equation 𝐝𝟐 𝛙 𝐝𝐱𝟐 + 𝐝𝟐 𝛙 𝐝𝐲𝟐 + 𝐝𝟐 𝛙 𝐝𝐳𝟐 + 𝟖𝛑𝟐 𝐦 𝐡𝟐 (𝐄 −𝐕)𝛙 = 𝟎
• 4.
  Acceptable solutions tothe Schrodinger wave equation must have certain properties  Ψ must be continuous  Ψ must be finite  Ψ must be single valued  0 ∞ Ψ𝟐 = 1
• 5.
  Continuous and noncontinuousfunction -1 -0.5 0 0.5 1 0 100 200 300 400 sin(θ) -6 -4 -2 0 2 4 6 0 100 200 300 400 tan(θ) Continuous function noncontinuous function θ θ
• 6.
  Finite and infinitefunction A = {0, 1, 2, 3,4, 5} finite set A = {0, 1, 2, 3,4, 5,……} infinite set  𝑓(𝑥) = 𝑥 + −1𝐴 = 𝜋𝑟2  𝑓(𝑥) = 𝑥 0  𝑓(𝑥) = 𝑥2 ×(∞)
• 7.
  -10 -5 0 5 10 0 20 4060 80 100 More than one value for the function y x At same value of x, we observe two different value of Y 𝑦2 = 4𝑝𝑥 27
• 8.
  Integrating function froma to b Integrating any function gives area under the curve formed by that function 𝑎 𝑏 𝑓𝑥 𝑑𝑥 = 𝑎𝑟𝑒𝑎 3 4 π 1 2 π 1 4 π π 0π 0.314 0.314 0.314 0.314 0.314 0.314 0.314 0.314 0.314 0.314 0 0.4 0.8 0 π 𝑠𝑖𝑛𝑥 𝑑𝑥 = 2 𝑓(𝑥) = 𝑠𝑖𝑛𝑥
• 9.
  Function and functionsquare -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 0 100 200 300 sin(θ) or [sin(θ)] 2 θ
• 10.
  End note Several wavefunction satisfy these properties and each of these have corresponding energies. These wave functions are called orbitals. In hydrogen atom the wave function which has lowest energy level(E1) is 𝝍1. There are number of acceptable solutions of the wave function and each orbital is described by set of three quantum numbers n, l and m.