Notation Definition and 1000 Threads

QUESTION A quantum mechanical system has a complete orthonormal set of energy eigenfunctions, |n> with associate eigenvalues, En. The operator \widehat{A} corresponds to an observable such that Aˆ|1> = |2> Aˆ|2> = |1> Aˆ|n> = |0>, n ≥ 3 where |0> is the null ket. Find a complete...

So let's take a hexagonal crystal. The term: C6 then refers to the 6-fold rotation group. I litterarily have no idea about what a group is but still want to understand the basic things qualitatively. So what is meant by the 6-fold rotation group? Is it the set of 6 fold rotations leaving the...

I'm wanting to write, \vec{a} = \dot{v} But I don't think this is entirely correct. Is there a standard shorthand for this?

given: at t=0 |PSI(0)> = 1/2 |PSI1> + (SQRT3)/2 |PSI2> --------------------------------------------------------------------- my attempt so far: we can write |PSI1> = 1/2 |UP> + 1/2 |DOWN> |PSI2> = (SQRT3)/2 |UP> + (SQRT3)/2 |DOWN> therefore |PSI(0)> = 1/2 |UP> + 1/2...

Homework Statement I'm trying to wrap my head around series notation, but I'm finding some of the transformations hard to grasp. For example, this one: Homework Equations \Sigma^{n}_{i=1} (2a_{i}-3) = 2\Sigma^{n}_{i=1}a{_i}(-3n) The Attempt at a Solution In the above expression, I...

I have 2 ket vectors that i need to prove are orthogonal and normalised I know <Up|Down> = <Down|Up> = 0 <---- Orthogonal Condition I know <Up|Up> = <Down|Down> = 1 <---- Normalisation Condition My problem is I have 2 ket vectors, say |A> and |B>, containing |Up> and |Down> terms. How do I...

Is it just ∇-1 with the vector hat?

I never really understood leibniz notation. I know that dy/dx means differential of y with respect to x, but what do the 'd's mean? How come the second-order differential is d2y/dx2? What does that mean? And what does d/dx mean?

A week or two ago we went through index notation in class, however I didn't understand it when the lecturer was going through it thus I need to go through it now. I have this weekend to go through it along with other material. Is it possible to go over basic index notation in this short period...

Hi everyone, my problem is this Using Dirac notation show that \frac{d}{dt}<\varphi|\hat{A}|\varphi> = \frac{i}{\hbar}<\varphi|[\hat{H},\hat{A}]|\varphi> where A does not explicitly depend on t I am given as a hint that the hamiltonian operator in Dirac notation is...

If I have two 3 dimensional position vectors: s and v What is the notation for the distance between them? I know to calculate the distance I would use: r = SQRT ( (s1-v1)^2 + (s2-v2)^2 + (s3-v3)^2 ) where s1 is the first element in the position vector s etc. What is...

hi all, I got a question about the spelling difference on a particular case. I registered to address my problem to native English speakers(or people who can help me :)). Hopefully this is the right part of the forum. Currently i am writing my thesis in English(i am not a native English...

I have this pass paper question I am trying to do and I can't even get started, Have been doing vector sums and just started bows notation. I don't want a solution just where do I start. what's my first move? Question is attached the fact I have only one force is throwing me out.

I am reading an article about Minkowski space (as a vector space, which is why I am putting my question in this rubric) which is poorly translated from the Russian, and have come across several notational curiosities, most of which I have been able to figure out. However, there is one that I do...

In a paper translated from the Russian, the author refers to "m-m" and "n-n" circles (including Minkowski circles) and orbits. When I first came across "n-n", I thought it was "non-negative" until I came across the "m-m". In one of the references I went to a diagram referred to, and saw an arc...

1.) an inner product of a state vector represent by <\psi|\psi>. sometimes the notation is like <\phi|\psi> is mean transfer from state |\psi> to <\phi|.it mean the former 1 do not transfer the state? what is the difference between both? 2.) what is mean by <x|\psi>? is it mean x(position)...

How do I read, interpret the following definitions for the expectation of a random variable X? Assume the integral is over the entire relevant space for X. (1) E(X) = ∫ x dP (2) E(X) = ∫ x dF(X) If I asked you to calculate (1) or (2) for an arbitrary X, how does it look? My only other...

Zee writes in Einstein Gravity in a nutshell page 186 "let us define the transpose by ##(\Lambda^T)_\sigma^\mu = \Lambda_\sigma^\mu##" and even emphasizes the position of the indexes. Yes, they are not exchanged! This must be a typo, right?

Hello, when we have a deterministic signal f:ℝ→ℝ that is square integrable we can typically write f \in L^2(\mathbb{R}). However, what if \{ f(t): \; t\in \mathbb{R} \} are random variables, i.e. f is a continuous-time stochastic process? What is the notation to denote the space of "square...

Hi there, During a recent tutorial, I asked my tutor about the notation he uses for vectors - he draws the little half arrow above them and I was curious whether that was significant, as opposed to just underlining vectors. He said it was a mathematical technicality and suggested I look up...

If X is a Euclidean subspace, what does Fr(X) mean? I have been unable to find any references to this notation, so any help would be appreciated.

Hey, I was wondering if anyone had any recommendations for books that provide an introduction or a detailed explanation on the whole 4 vectors, tensors and using indicial notation (in the context of General Relativity or Quantum Field) - basically anything that explains to me how to...

Homework Statement use the relationship ε_{ijk} ε_{klm}=δ_{il}δ_{jm}-δ_{im}δ_{jl} to find an alternative expression for ε_{ijk}ε_{ilm}. Hence simplify ε_{ijk}ε_{ijm} 2. Homework Equations I know that the kronecker delta is 1 for i=j and 0 for i not equal to j. and that the alternating...

Just going over my linear algebra notes and I've forgotten the formal definition of ## \epsilon(i,j)_{rs} ## I have written down ## \epsilon (i,j)_{rs} = \delta_{ir}\delta_{js} ## but I can't seem to remember what r and s represent. Also, I don't quite understand why it equals ##...

Greetings, There is an aspect of tensor-index notation that I want to know more about. For a simple example, let M be a 1-1-tensor (ie., a matrix), whose elements can be indexed by Latin letters. What is the difference between the component M^a_{\hspace{2mm}b} and the component...

Homework Statement Hi all, Here's the problem: Prove, in tensor notation, that the triple scalar product of (A x B), (B x C), and (C x A), is equal to the square of the triple scalar product of A, B, and C. Homework Equations The Attempt at a Solution I started by looking at the triple...

For example my textbook reads if G(V, E) is a pseudograph then \sum\limits_{v \in V} deg(v) = 2|E|

I have a homework problem discussing the heat equation, and I have two questions about notation that I could not figure out through google searching: L^1(ℝ) as in a function g\in C^1(ℝ)\cap L^1(ℝ) ||u(\bullet ,t)||_{L^∞} The bullet in the second expression is actually a single dot at that...

Hi I am looking for the proper notation to represent angle wrapping in a mathematical function. For example if I have a function of the form: y=exp(θ) (and θ is an angle in degrees.) How do I write this function to explicitly assert that: -180 ≤ θ < 180 ? So that for example if...

Homework Statement A steel ball is fired from a ballistic launcher at different angles. The launched ball has been found to travel from the edge of a table to land 30.0 cm from the far end of the table when starting from the height of the table and launched at an angle of 30.0◦ above the...

Homework Statement Using Leibniz's rule to find dy/dx for y = integral of e^-t from interval: [ln(x) to ln(x+1)]Homework Equations The Attempt at a Solution dy/dx = e^-(ln(x+1))*(1/(1+x))-e^-(ln(x))*(1/x) = (x+1)/(1+x) - (x/x) = 0 Im not sure what I'm doing wrong or how to properly use...

http://img59.imageshack.us/img59/6414/puag.png The picture above is used to help understand artificial neural networks, however for now this doesn't matter as I'm only concerned with the maths. A number is input at the start of each both horizontal lines at the left hand side. The numbers...

Homework Statement We will see (in Chap. 5) that the magnetic field can be derived from a vector potential function as follows: B = ∇×A Show that, in the special case of a uniform magnetic field B_{0} , one possible vector potential function is A = \frac{1}{2}B_{0}×r MUST USE TENSOR NOTATIONm...

I am new to tensor notation, but have known how to work with vector calculus for a while now. I understand for the most part how the Levi-Civita and Kronecker Delta symbol work with Einstein summation convention. However there are a few things I'm iffy about. For example, I have a problem where...

So all my life I have disliked writing in scientific notation's notation as mx10n where m and n are constants, because it looks indistinguishable from m times x times 10 to the n power. Alternatively it looks like the cross product of m and 10^n, which makes little sense because m and n are not...

Everything I've encountered in physics so far allows infinitesimal numbers to be manipulated as real numbers. But there has been much criticism towards Leibniz's notation, and I assume it is for a reason. When in mathematics will the infinitesimal notation not work? Including treating...

Hello, I consider the permutations \sigma_i, where i\in \{1,\ldots,n\}, of the following kind: \sigma_i is obtained by choosing the i-th element from (1,..,n) and by shifting it to the first position; for instance \sigma_3 = (3,1,2,\ldots,n). The parity of \sigma_i is clearly (-1)^{i-1}. For...

Since \frac{dy}{dx} is just considered notation, how can we treat it as an actual fraction when soliving differential equations? Could you, for instance, replace \frac{dy}{dx} with y'(x) in a differential equation and work it out?

Homework Statement http://i.minus.com/jbiWoIFy45kCgV.png Homework Equations The denominator of a function cannot equal 0. Both the numerator and denominator also cannot = 0 simultaneously. The Attempt at a Solution For the first problem, the denominator and the numerator are 0...

could B d/dt (x1 -x2) be equal to B (dot{x}1 - dot{x} 2)? Thank you! dot{x} is supposed to be a "dot" over a x. Just a formatting problem

So dx means an infinitesimally small change in x. Why is the slope written \frac{dy}{dx} instead of \frac{f(x)}{dx} since you are only making the x component infinitely small? When you take the integral you do ∫f(x)dx not ∫dy*dx

Why is it that the norm of a vector is written as a "double" absolute value sign instead of a single one? I.e. why is the norm written as $ || \vec{v} || $ and not $ | \vec{v} | $? I think $ | \vec{v} | $ is appropriate enough, why such emphasis on $ || \vec{v} || $? I think it's rather natural...

Hi everyone! I'm very new to combinational logic design and this is a question on an assignment that we've been given. This particular situation wasn't covered in lecture material so I've been Googling and trying to think abstractly about it but I'm pretty stuck for an approach. And I'm not...

I'm a little confused about what is actually meant by the JP = 1/2 + octet. I'm pretty sure it means the particles must have spin 1/2 in the ground state (l=0) and an even parity but what I'm confused over is the absence of an sss, uuu or ddd state. I understand that this would give I3 = 3/2...

Homework Statement Hi All, I was trying to write that ## I ## is unique. ##I ## is my identity element. Homework Equations The Attempt at a Solution Maybe I can write ## \exists I | I = I ## ##\forall I \in G ## Except with spaces. Is this not a way? Just trying to...

Quick question: When we write an integral ##\displaystyle \int\limits_U f(x^1,\dots, x^n)~dx^1\wedge\cdots\wedge dx^n##, we really mean ##\displaystyle \int\limits_U f\wedge dx^1\wedge\cdots\wedge dx^n##, right?

Hi, I want to be able to say the following with mathematical symbols; 1) A is any integer. 2) A is a non-integer (not a whole number). Please help. Thanks

I was reading a journal article from the 50s and came across some calculus notation that I do not know. Here is a link to the equation: http://i41.tinypic.com/s12k1t.jpg In equation 19, the constants A and B are shown on top of each other (same with cos[mθ] and sin[mθ]). What does this...

Difficulty regarding notation for Lorentz transformation Please can somebody explain to me the relation between Δ^{σ}_{μ} and Δ_{σ}^{μ} as symbols representing a Lorentz transformation? Thanks.

Homework Statement If |A> = x |B> + y |C> where |B> and |C> are orthonormal, then what happens when <A|A> ?The Attempt at a Solution Would <A| = x* <B| + y* <C|? I'm not really sure where to go from there