Numbers Definition and 1000 Threads

I am reading a book about the interaction between atom and photon. I don't understand the following statement: "for the sake of simplicity, we assume the atom to be infinitely heavy and disregard the external quantum numbers" Q: what is the external (or internal) quantum number of an atom.

Physics Lab -- greatest common factor between all these numbers Homework Statement Hey, how can I find the greatest common factor between all these numbers? Please reply as soon as possible, it is an assignment due tomorrow. 27.69 3.15 0.59 4.71 18.08 22.84 31.08 19.11 21.91 9.7 38.78 42.82...

Are the less than (<) and greater than(>) relations applicable among complex numbers? By complex numbers I don't mean their modulus, I mean just the raw complex numbers.

If counting/positive numbers exist, do they imply the existence of negative numbers? I'd say yes, because there's always a bijection that maps the lowest counting number of the set to the highest, then the second lowest to the second highest, etc. This reversal of order/mirroring is possible...

Homework Statement Prove that if one chooses more than n numbers from the set {1,2,3, . . . ,2n}, then one number is a multiple of another. Can this be avoided with exactly n numbers? The Attempt at a Solution If we pick the top half of the set n+1 up to 2n we will have n numbers that are...

If a is a complex number, and a^2-a+1=0, then a^2011=? I tried using De Moivre's theorem, Taking a=cosθ+isinθ, but didn't get anywhere, got stuck at cos2θ+isin2θ-cosθ-isinθ+1=0. What do I do?

show that in a set of any 5 consecutive numbers there is at least one number that is co-prime to all the rest 4 (for example (2,3,4,5,6- 5 is co-prime to 2,3,4,6)

Guys, please help me figure this out: 1) how to calculate the largest prime less than 300 2) why 35 and 37 are not twin primes? 3) the smallest number divisible by five different primes Any input would be greatly appreciated)

I'm not sure whether this should go in this forum or another. feel free to move it if needed Homework Statement Suppose that z_0 \in \mathbb{C}. A polynomial P(z) is said to be dvisible by z-z_0 if there is another polynomial Q(z) such that P(z)=(z-z_0)Q(z). Show that for...

Hi everyone, I have studied QFT, the SM and the Higgs mechanism when I was in university and after reading an article from CMS (CERN) about the spin-parity measurement of the HZZ channel, which shows that J^{P}=0^+ is favoured versus J^{P}=0^-, I went back to the theory of the Higgs boson...

Is the set of the natural Nos complete?

Here is the question: I have posted a link there to this question so the OP can view my work.

Homework Statement Why isn't (3, -2 , 0 , 1/2) a valid quantum number? Homework Equations The Attempt at a Solution n=3 so l = -2 is valid. -l≤Ml≤l 2≤Ml≤-2 nonsensical statement. I don't know what to do...

Problem: All 4 digit numbers of the form $x_1x_2x_3x_4$ are formed by using digits $1,2,3,4,5,6,7,8,9$ such that $x_1\leq x_2 \leq x_3 \leq x_4$. a)Find the total number of such possible 4-digit numbers. b)The numbers are written in ascending order. If the number with rank 460 is abcd, then...

Hello, Homework Statement The complex numbers z_{1} = \frac{a}{1 + i} and z_{2} = \frac{b}{1+2i} where a and b are real, are such that z_{1} + z_{2} = 1. Find a and b. Homework Equations The Attempt at a Solution This looked like a time for partial fractions to me, so I went...

Problem: Let $\dfrac{1}{a_1-2i},\dfrac{1}{a_2-2i},\dfrac{1}{a_3-2i},\dfrac{1}{a_4-2i},\dfrac{1}{a_5-2i}, \dfrac{1}{a_6-2i},\dfrac{1}{a_7-2i},\dfrac{1}{a_8-2i}$ be the vertices of regular octagon. Find the area of octagon (where $a_j \in R$ for $j=1,2,3,4,5,6,7,8$ and $i=\sqrt{-1}$). Attempt...

Homework Statement I have to find the Thevinin Equivalent for the following circuit. I am assuming the current is going out of the node. V= node between inductor and capacitor V0 = V[40/(40-150j)] (V-75)/(600+150j) + (-0.02V0) + V/(40-150j) = 0 The only problem I have is with the last...

Homework Statement Suppose that u and v are real numbers for which u + iv has modulus 3. Express the imaginary part of (u + iv)^−3 in terms of a polynomial in v.Homework Equations The Attempt at a Solution |u+iv|=3 then sort(u^2+i^2) = 3 then u = 3 and v=0 or u=0 and v=3(0+3i)^-3 i swear i am...

$x,y\in R$ $if: \sqrt {3x+5y-2-m}+\sqrt {2x+3y-m}=\sqrt {x-200+y}\,\times\sqrt {200-x-y}$ $find:\,m=?$

Homework Statement problem in a pic attached Homework Equations The Attempt at a Solution i solved i and ii a , when it came to b , i just said that every one of the 3 roots will be squared having 2 roots 1 + and 1 - but then i read the marking schemes ( also attached) , and i got...

Wikipedia is not very clear on this. Is there a known computable normal number? I found this paper: http://www.glyc.dc.uba.ar/santiago/papers/absnor.pdf But I'm not sure if it's been peer reviewed.

What is the significance/physical interpretation of Fractional Occupation Numbers in DFT?

Homework Statement Prove the formula xcscx=2B(ix)-B(2ix)Homework Equations B(x)=x/((ex)-1) sinx= (eix-e-ix)/2i The Attempt at a Solution I know that it makes sense to use the formula for B(x) with x=ix and x=2ix, and rewrite xcsc(x) as x/sin(x), plugging the above relevant equation in for...

I want to solve y''+y'+y=(sin(x))^2 and try to use y=Ae^{ix} but then when I square it I get A^2 e^{2ix} I found y' and y'' and solved for A and it didn't work I guess I could use the formula for reducing powers but I would like to try and get around that.

Parition function for Boson "gas" with two quantum numbers Let's say that we have a system of non-interacting Bosons with single-particle energies given by, \epsilon_{p,m} = \frac{p^2}{2m} + \alpha m where m = -j, ... ,j and we want to calculate the partition function of this...

Okay, so this is a problem I've been pondering for a while. I've heard from many people that pi doesn't repeat. Nor does e, or √2, or any other irrational or transcendental number. But what I'm wondering is, how do we know? If there truly is an infinite amount of digits, isn't it bound to...

Homework Statement Let f(z) = z3-8 and g(z) = f(z-1). This information applies to questions 1-5. 1. Express g(z) in the form g(z) = z3+az2 +bz + c 2. Hence, solve g(z) = 0. Plot solutions on an Argand diagram. Homework Equations Factorisation i2=-1 The Attempt at a Solution I have done...

Homework Statement Hello Assume that we have n complex numbers u: u_1,u_2,...,u_n, and n complex numbers v:v_1,v_2,...v_n I would like to prove that: |\Sigma_{i=1}^nRe(u_i\bar{v_i})| \le |\Sigma_{i=1}^nu_i\bar{v_i}| I guess this can be written simpler: |\Sigma_{i=1}^nRe(z_i)| \le...

Hello :smile: Homework Statement The orbital quantum number for the electron in the hydrogen atom is l = 4. What is the smallest possible value (in eV) for the total energy of this electron? (Use the quantum mechanical model of the hydrogen atom.) Homework Equations The Attempt at a Solution...

Hello my name is Dax, I'm currently in the world building stage of a science fiction I am writing and I came here to bounce some questions off of you fine people. My question is regarding atomic numbers of elements on the periodic table and weather it could be possible that negative atomic...

Find natural numbers a and b such that $2^a-3^b = 7$

Homework Statement This is the solution, the question was find its domain. Homework Equations How does |X| (less than or equal to) 4, when a negative number is inputed into -2x how does that = a positive number?The Attempt at a Solution On the graph to me All X values < 0 should be negative...

Solve in real numbers the equation $\sqrt[3]{a-1}+\sqrt[3]{a}+\sqrt[3]{a+1}=0$

can you help me solve this just using one variable the sum of two numbers is 9 and their difference is 6. what are the numbers? thanks!

I noticed that there are some odd looping numbers in pi Following the rule that : the string becomes the position which becomes the string ( I'll use " Sn " for string number and " Pn " for position number, ( after the decimal ) becomes the next string to locate ( Sn → Pn → Sn ) The process is...

Homework Statement Is there a real number c such that the series: ∑ (e - (1+ 1/n)^n + c/n), where the series goes from n=1 to n=∞, is convergent? The Attempt at a Solution I used the ratio test by separating each term of the function as usual to find a radius of convergence, but that doesn't...

The problem is as stated: Prove that F_1*F_2+F_2*F_3+...+F_{2n-1}*F_{2n}=F^2_{2n} But earlier in my text I proved by induction that F_{2n}=F_1+F_2+...+F_{2n-1}. Do I need to use this earlier proof in my current proof. I tried adding F_{2n+1}F_{2n+2} to the right and left hand side of the first...

I have been looking at material properties such as thermal expansion of metals which usually involves very small coefficients. The general equation of thermal expansion is usually L_\theta = L_0 ( 1 + \alpha \theta) where L is the length and theta is the temperature change. The coefficient...

I just finished reading the "Reality Bits" in a recent copy of NewScientist. It discusses attempts to purge mathematics of the need for complex numbers. Started me thinking(danger, danger) of not how to get rid of the square root of negative one, but, more easily, simply find out where it enters...

Homework Statement Solve the equations: 3(z-2) = 2j(2z+1) and (i-2)z-z*=3i+1 where z* is the complex conjugate of z. (I am assuming z and z* are the unknowns. i and j are basically the same since they're defined as i2 = j2 = -1?) Homework Equations Rules for solving...

this is the program which i wrote: #include<iostream.h> #include<conio.h> #include<stdlib.h> void prime(int p) { if(p==0||p==1) { cout<<"neither prime nor composite"<<endl; getch(); exit(1); } for(int i=2;i<p/2;i++) { if(p%i==0) { cout<<"composite"<<endl; break; } else...

I understand the definition of real numbers in set theory. We define the term "Dedekind-complete ordered field" and prove that all Dedekind-complete ordered fields are isomorphic. Then it makes sense to say that any of them can be thought of as "the" set of real numbers. We can prove that a...

Hi, We know that if we have two complex numbers in polar format (i.e., magnitude and exponential), that for two complex vectors z1 = A*exp(iB) z2 = C*exp(iD) If z1 and z2 are equal, then A = C and B = D. However, this is assuming these values are all real. What if they are complex...

Hi everyone, i am just wondering why I cannot find a list of Charge Conjugation and Parity numbers for all the appropriate particles? I mean, I can look online and sift through sources for individual particles (for example, after some research I have found the the photon has a charge...

Hello everyone, I'm new to this forum. I have this Linear Algebra question that I have no clue how to solve. Any help would be much appreciated. :) The question goes as follows: The polynomial p(x) = x3 + kx + (3 - 2i) where k is an unknown complex number. It is given to you that if p(x) is...

1.1 Among the digits 1,2,3,4,5 first one is chosen, and then a second selection is made among the remaining four digits. Assume that all twenty possible results have the same probability. Find the probability that an odd digit will be selected. $\frac{3}{5}$ The second time $\frac{3}{5}$ The...

Homework Statement . Prove that, given constants ##A_1,A_2, \phi_1## and ##\phi_2##, there are constants ##A## and ##\phi## such that the following equality is satisfied: ##A_1\cos(kx+\phi_1)+A_2\cos(kx+\phi_2)=A\cos(kx+\phi)## The attempt at a solution. I've tried to use the...

Hello I am writing a program where program will randomly generate a three digit number from 100 to 999 and then user will be asked to guess that number. If the number is matched exactly, then the highest prize is given to the user, if all digits in a guess are also in the original number...

I am studying programming for the first year so I don't have whole lot of experience. I am interested in how to work with super-large numbers, numbers that are much, much larger then the included Int or _int64. I mean some 100, 1000 .. 17 million (largest prime) digit numbers. How do they do...

I talked with an old friend of mine. We discussed prime numbers and Ulams Spiral, and the mathematical patterns that surround us all. He brought up something called the Zeta-Function and something about -1 1/2 and how this all related to prime numbers. I did a google search and found some...