Question

The complex forms for the spherical harmonics with l­=3 and ml= +3 and -3 are: Y33...

The complex forms for the spherical harmonics with l­=3 and ml= +3 and -3 are:

Y33 = N­sin3θei3φ and Y3-3 = N­sin3θe-i3φ. Using the Euler expansion on the negative exponentials, show how the linear combination Y33+ Y3-3results in a real function, and the linear combination
–i(Y33- Y3-3) result in a different real function. Are these real functions orthogonal to each other? Explain

Science   Advanced-Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A) Iron(II) forms what is termed a “charge transfer complex” with the 1,10-phenanthroline. What is meant...
A) Iron(II) forms what is termed a “charge transfer complex” with the 1,10-phenanthroline. What is meant by this term and why are such complexes highly colored (i.e. how/why is the absorption of light so favored at their characteristic wavelength)? (Note: your textbook specifically discusses the iron-1,10-phenanthroline complex; be careful – it is an exception to some generalities about charge transfer complexes.) (0.5) 3 B) Iron(III) also forms a complex with the phenanthroline ligand; explain why it cannot form a charge...
If p(x) is a complex polynomial with real coefficients, it is well known that it can...
If p(x) is a complex polynomial with real coefficients, it is well known that it can be factored into a product of linear and quadratic terms with real coefficients, or into a product of linear terms only if the coefficients are allowed to be complex. First, use Maple to write q(z) = x5 −3x4 −3x3 +9x2 −10x+30 as a product of exact linear and quadratic factors with real coefficients. By exact, I mean you should leave any non-rational factors expressed...
Problem 3 Countable and Uncountable Sets (a) Show that there are uncountably infinite many real numbers...
Problem 3 Countable and Uncountable Sets (a) Show that there are uncountably infinite many real numbers in the interval (0, 1). (Hint: Prove this by contradiction. Specifically, (i) assume that there are countably infinite real numbers in (0, 1) and denote them as x1, x2, x3, · · · ; (ii) express each real number x1 between 0 and 1 in decimal expansion; (iii) construct a number y whose digits are either 1 or 2. Can you find a way...
3. The economy is made up of two types of agents: There are 4000 people in...
3. The economy is made up of two types of agents: There are 4000 people in group 1 and each of them have the utility function U1 = W3/4 The income for everyone in group 1 is such that they have a 75% chance of making $50 and a 25% chance of making 300. Group 2 has 6000 people and each have the utility U2 = W1/3. The income for these people is that they have a 30% chance of...
1. Consider the general form of the utility for goods that are perfect complements. a) Why...
1. Consider the general form of the utility for goods that are perfect complements. a) Why won’t our equations for finding an interior solution to the consumer’s problem work for this kind of utility? Draw(but do not submit) a picture and explain why (4, 16) is the utility maximizing point if the utility is U(x, y) = min(2x, y/2), the income is $52, the price of x is $5 and the price of y is $2. From this picture and...
In this question, you will carry out the algebraic equivalent to the diagrammatic analysis investigating the...
In this question, you will carry out the algebraic equivalent to the diagrammatic analysis investigating the effect of amenities on incomes and real-estate prices. To start, let the consumer utility function be given by q1/2c1/2a1/2, where c  is consumption of “ bread ” (a catch-all commodity), q is real estate (housing), and a is amenities, which are valued by the consumer given that a’s exponent is positive. Letting y denote income, it can be shown that the consumer demand functions for...
I tried using the modulo to skip the chars but I doesnt work in some cases....
I tried using the modulo to skip the chars but I doesnt work in some cases. There are two ways to write loops: (1) iterative, like the for-loops we're used to using, and (2) recursive. Your prerequisite preparation for this course should have exposed you to both, although your working knowledge of recursive loops may not be as strong as that of iterative loops. Consider the following iterative function that prints an array of characters backward: #include #include // print...
There are two ways to write loops: (1) iterative, like the for-loops we're used to using,...
There are two ways to write loops: (1) iterative, like the for-loops we're used to using, and (2) recursive. Your prerequisite preparation for this course should have exposed you to both, although your working knowledge of recursive loops may not be as strong as that of iterative loops. Consider the following iterative function that prints an array of characters backward: #include <iostream> #include <cstring> // print an array backwards, where 'first' is the first index // of the array, and...
Adder Start out by picking 2 positive six bit binary numbers that are less than 3210,...
Adder Start out by picking 2 positive six bit binary numbers that are less than 3210, written in 2's complement notation. The eventual goal is to add these two numbers. 1) Look at the LSB bit of the numbers, and using logic gates (NANDs, NORs, etc.) design a circuit that correctly gives the right output for any possible combination of bits in the LSB place. 2) Now look at the next column to the left (next to LSB). In this...
In a small-scale regression study, we collected data on the number of children in a family...
In a small-scale regression study, we collected data on the number of children in a family Xi and the number of hours per week spent shopping Yi. The following data were obtained: i 1 2 3 4 5 6 Xi 2 6 3 1 1 9 Yi 13 17 12 12 9 22 Assume we performed a simple linear regression of Yi on Xi, i.e. E(Yi) = ?0 + ?1Xi (a) By hand compute X?X, X?Y, (X?X)-1, b, Y^(means Y-hat),...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT