What is L if n=2 and l=0? Taking into consideration that L is an associated Laguerre polynomial.
What is L if n=2 and l=0? Taking into consideration that L is an associated Laguerre...
(20 pts.) The Laguerre differential equation is ry" + (1 - )y' + Ay = 0. (a) Show that x = 0 is a regular singular point. (b) Determine the indicial equation, its roots, and the recurrence relation. (c) Find one solution (x > 0). Show that if = m, a positive integer, this solution reduces to a polynomial. When properly normalized, this polynomial is known as the Laguerre polynomial, L. (2).
Problem 2. The Laguerre polynomials L (x) are orthogonal with respect to the inner product (u,u)=/o e-ru (x) u(x) dx and standardized so that L" (0) = 1 . In addition to their importance in numerical analysis, the La- guerre polynomials are notable for their use in electron orbitals in atoms Use Gram-Schmidt orthogonalization along with the standardization L(0)1 to find the Laguerre polynomials of degree ns4 The Laguerre polynomials obey the TTRR (n + 1) L" +1 (x) =...
The differential equation X2 - x) dx +ny = 0) is known as Laguerre's equation. a) Obtain the regular solution in the form y(a)= B, 1+ (=nye mcn = 5125" (n=k+1}x k=1 b) Show that this solution is a polynomial of degree n when n is a nonnegative integer, and verify that the choice B. = 1 leads to the Laguerre polynomial of degree n, with the definition - ... + n! L,(x)=1 – () * + (3) ... +47*...
1. The following cash flows are associated with three alternatives under consideration by the firm: N (Year) 0 2 3 4 5 A1 (TL) 0 4,500 4,500 4,500 4,500 4,500 A2 (TL) -50,000 20,000 20,000 20,000 20,000 20,000 A3 (TL) -75,000 20,000 25,000 30,000 35,000 40,000 If interest rate for the firm is 12%, compare the alternatives using the internal rate of return method (IRR method) and incremental cash flow approach. Which alternative should be selected? Why?
What is 1 example of an ethical consideration associated with Maternal mortality?
What type of orbital (i.e.,3s,4p,...) is designated by these quantum numbers? A) n=4,l=1,ml=0 B) n=2,l=0,ml=0
After taking into consideration a couple's AGI in 2019, the couple's American opportunity credit and lifetime learning credit are $5,000 and $1,800, respectively. The couple's refundable and nonrefundable education credit is: 1. $5,000 and $1,800 2. $0 and $6,800 3. $3,000 and $3,800 4. $6,800 and $0 5. $2,000 and $4,800
SECOND PART OF QUESTION -WHAT VALUES OF N?
2. Write the Taylor polynomial of degree n for the function f(x) = 5 centred at a > 0. For given remainder R > 0, what values of n guarantee that the error term of the polynomial is less than R? 2. Write the Taylor polynomial of degree n for the function f(x) = centred at a > 0. For given remainder R > 0, what values of n guarantee that the...
What is the state label for a 4dz2 orbital? A) n=4, l=0, ml = -1 B) A n=4, l=1, ml = -1 C) A n=4, l=2, ml = -1 D) n=4, l=1, ml =0 E) A n=4, l=2, ml =0
Consider an electron in a hydrogen atom in the n=2, l=0 state. At what radius (in units of a0) is the electron most likely to be found?