What is the significance of d (x^2-y^2) in the d subshell?

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In summary, The d (x^2-y^2) orbital is named after the angular part of the x^2-y^2 function in the Schrödinger wave equation. This function can be derived using the trigonometric functions in the spherical harmonics and is used to visualize the orbital. Online resources are available for further information.
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americast
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Hi all,
One of the orbitals of the d subshell is called d (x^2-y^2). What is the reason behind that? It would be helpful if someone could give the calculations.

Thanx in advance...
 

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  • #2
It is simply the angular part of x^2-y^2. Use ##x=r \sin \theta \cos \phi## and ##y=r\sin \theta \sin \phi##.
 
  • #3
While any decent quantum chemistry or quantum mechanics book should have the calculation for you, I did find http://www.fordham.edu/images/undergraduate/chemistry/pchem1/spherical_harmonics.pdf online that should do the trick. There's plenty online on (visualization of) the spherical harmonics, so if you need more information on them in particular, shouldn't be too hard to find.
 
  • #4
This is actually the wave function obtained after solving Schrödinger wave equation and by comparing linear part of the function with mathematical trigonometric functions it looks like the squad of rectangular coordinate x minus square of rectangular coordinate y
 

What is d (x2-y2)?

D (x2-y2) is a mathematical notation used to represent a type of equation in algebra. It is also known as the difference of squares.

Why is it called d (x2-y2)?

The notation d (x2-y2) is derived from the word "difference", which represents the subtraction operation in this equation. The "x2" and "y2" refer to the exponents of the variables x and y respectively.

What is the purpose of d (x2-y2)?

D (x2-y2) is used to factorize quadratic equations in the form of (x2-y2). This allows us to find the roots of the equation and solve for the values of x and y.

How is d (x2-y2) related to the Pythagorean theorem?

D (x2-y2) is closely related to the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. By using d (x2-y2), we can easily factorize and solve for the values in this type of equation.

Can d (x2-y2) be used in other types of equations?

Yes, the notation d (x2-y2) can be used to solve for the roots of other types of equations with two variables, as long as they are in the form of (x2-y2). However, it may not always be the most efficient method for solving these equations.

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