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-1
votes
1answer
21 views

L-S Coupling (Atomic Physics) Ground State [on hold]

Can someone please explain to me why in the second configuration the ground state is associated with $L=F=3$ and $J = 7/2 $? ** Another question: Should we always take $J$ as even? if yes, why?
0
votes
1answer
54 views

Notation of integrals

Hi I am relatively new to quantum mechanics. I encountered a certain use of notation which I am curious about, I will provide the context and question now: We have the basis $\{ | \vec{r} \rangle \} ...
-3
votes
1answer
61 views

Writing Tensor in LaTeX [on hold]

How can I write this in LaTeX? Each time I am trying to write it down the compilers is showing me error for multiple subscription.
1
vote
0answers
26 views

Question about notation in a simple circuit [on hold]

I was given this circuit in an Electricity & Magnetism course. On the far left, is that a current source providing 2A? It seems to be but I'm not 100% sure.
5
votes
1answer
78 views

Staggered Indices ($\Lambda^\mu{}_\nu$ vs. $\Lambda_\mu{}^\nu$) on Lorentz Transformations

I have some open-ended questions on the use of staggered indices in writing Lorentz transformations and their inverses and transposes. What are the respective meanings of $\Lambda^\mu{}_\nu$ as ...
1
vote
1answer
91 views

How does the Einstein summation convention apply to the following equation?

This is the equation is in the "mathematical form" section of the following wikipedia article: http://en.wikipedia.org/wiki/Geodesics_in_general_relativity More specifically, the "Full geodesic ...
3
votes
2answers
45 views

Variation of Lagrangian density $\mathcal{L}$ w.r.t $x_\mu$

If a function $f(x(t),y(t))$ has no explicit dependence on the variable $t$, then $\frac{\partial f}{\partial t}=0$. In quantum field theory, the Lagrangian density ...
-1
votes
1answer
43 views

Interpreting $\hat{e}_z$ in Maxwell's equations

I'm trying to interpret a form of Maxwell's equations, but I can't seem to figure out where the term $\hat{e}_z$ comes from in the following equation: $ ...
0
votes
1answer
41 views

Notation of a vector containing equation in a paper

I'm trying to implement Coulomb long range interactions into a molecular simulation program using a particle-particle/particle-mesh Ewald solver. The following equation from the paper "How to mesh up ...
2
votes
0answers
55 views

(Causal) Set notation round brackets vs square brackets? [closed]

In many (quite old) papers & books I have been reading recently in the causal theory of general relativity (e.g. On the structure of causal spaces, Kronheimer & Penrose, 1967) I find sets ...
4
votes
1answer
90 views

Indicating that indices are equal in Einstein notation

tl;dr: I have an expression like this: (dramatization) $$ R_{\mu\nu} = \begin{pmatrix} B^{00}C_{00} & 0 & 0 & 0 \\ 0 & B^{11}C_{10} & 0 & 0 \\ 0 & 0 & B^{22}C_{20} ...
3
votes
1answer
34 views

What are the units pm/K?

I can only think of picometres, but it doesn't seem to make sense. Here is the context, from the paper 'Towards Reproducible Ring Resonator Based Temperature Sensors', Klimov et al., Sensors & ...
0
votes
2answers
96 views

Unitary operators evolving the set of Pauli matrices

Consider the Heisenberg picture of Quantum Mechanics. For a two state system we have the Pauli matrices evolving according to the relation $$\sigma_i(t)=U^+\sigma_i(0)U$$ where $U=e^{-iHt/\hbar}$ and ...
0
votes
0answers
39 views

Different subscripts for $\nabla$ operators while deriving force on system of many particles

Consider a system of 4 particles in an external conservative field. So force acting on each particle is derived from potential energy $U(x,y,z)$of the particle+field system: Total (external) force on ...
1
vote
0answers
46 views

Conventions for propagators in Feynman diagrams [closed]

So far, I picked up the following rules for the propagators: Scalars: Dashed Fermions: Solid Abelian gauge boson: Wavy Non-abelian boson: springy Ghost: Dotted This made much sense to me until I ...
1
vote
1answer
40 views

What is $bfr$ in this expression?

I am reading 'Fundamentals of Quantum Mechanics' by Sakir Erokoc and came across this expression in relation to transition probabilities: $$\vec p=e \langle \psi_b |bfr|\psi_a \rangle$$ Which can be ...
0
votes
1answer
33 views

Can a sum of Pauli matrices be a real value?

In the page 2 of Quantum Annealing for Constrained Optimization, the authors introduced a constraint term under the Constrained quantum annealing (CQA) section. The ultimate goal is to work out a ...
0
votes
0answers
44 views

Extending projection operator to infinite-dimensional case

Hi I have a basic question regarding bra-ket notation. Given that $\{|e_n \rangle \}$ is a discrete orthonormal basis, $$\langle e_m | e_n \rangle = \delta_{mn}$$ then $$\sum_{n}|e_n \rangle \langle ...
0
votes
1answer
73 views

Dirac Notation With Comma

Does $\langle A,B\rvert$ mean $\langle A\rvert\langle B\rvert$? If so how is an operator applied to this in $\langle A,B\rvert \hat O $? For an example say the annihilation operator acting on ...
-1
votes
1answer
34 views

Symbol $p^{0}$ of particle [closed]

This is a very trivial question, but I cannot seem to find the answer anywhere in a textbook or the internet. My question is, what particle is represented by this symbol? $$p^{0}$$
11
votes
2answers
528 views

Tensor product in quantum mechanics?

I often see many-body systems in QM represented in terms of a tensor products of the individual wave functions. Like, given two wave functions with basis vectors $|A\rangle$ and $|B\rangle$, belonging ...
-1
votes
1answer
67 views

Dot product in index notation [closed]

This is a question about a small exercise I am trying to do in order to check if I am correct. Such type of quantities can appear in propagators in QFT. Since I am not an index expert I need some ...
3
votes
1answer
66 views

What does the direct sum symbol (i.e. $\oplus$) mean in the context of uncertainties

I've noticed the symbol $⊕$ used in a context I'm unfamiliar with. In several papers about the the calculation of the uncertainty of quantities measured with hadron colliders. For example the ...
0
votes
1answer
58 views

What is uppercase ${\cal O}$ in electrodynamics?

I'm a bit puzzled as to what the symbol ${\cal O}$ means in electrodynamics, I'm reading this paper here http://arxiv.org/abs/astro-ph/0404512. See equation 43 which is in page 12, what is this ...
1
vote
0answers
40 views

Are there any symbols left? [closed]

I have looked through most of the symbols used in physics and math. It seems like there are none left in the alphabet and the greek alphabet. Are we screwed if we find a new constant? Edit: How do ...
5
votes
2answers
315 views

Beta decay: is it OK that the products are not electrically neutral?

I'm just learning about radioactivity, and there's one thing I'm unclear about. Take $\beta -$ decay, for example. Since a neutron splits into a proton and an electron (and an anti neutrino), but ...
1
vote
1answer
42 views

Solving systems of equations using Levi-Civita and index notation?

I'm doing some self-studying out of Hughston and Tod's Introduction to General Relativity and I stumbled upon a few problems asking me to solve systems of equations using Levi-Civita and index ...
0
votes
1answer
53 views

When dealing with spinor indices, how exactly do we obtain the barred Pauli operator?

In the set of SUSY notes I'm following, the Pauli operator is given as: ${(\sigma^\mu)}_{\alpha\dot{\alpha}} = (I_2, \sigma^1, \sigma^2, \sigma^3)$. The antisymmetric tensor that lowers and raises ...
1
vote
1answer
41 views

Correct way to write Pauli matrices

This is purely a question of notation for the Pauli matrices. What is the correct way to write them for use as operators? Would I just write the vector of the matrices as a vector i.e ...
0
votes
1answer
96 views

The Lie derivative of the metric $g_{ab}$ and index notation

I don't quite know where to start this question. I'm essentially not understanding how to compute the Lie derivative of a given metric and vector. So I have the following definition: $$ ...
0
votes
0answers
50 views

Understanding Dirac equation notation

I'm trying to recover the Einstein energy-momentum relation from the Dirac equation. I'm given a solution wavefunction, $$\psi = u(E,\vec p) e^{i(\vec p\cdot\vec x - Et)}$$ with $$\vec u = ...
0
votes
1answer
42 views

Ordering of Contravariant and Covariant spinors. Understanding the spinor space

I've been referring to Pg.36-Pg.38 in Introduction to Supersymmetry by Wiedamann. For understanding the precise origin of dotted, undotted indices on Spinors. He starts off my saying that $M$ acts on ...
0
votes
1answer
34 views

Calculating motion of equation in tensor form

for the Lagrangian density $$\mathscr{L}=\frac{1}{2}(\partial_{\mu}A^{\mu})^2$$ how can I get this $$\frac{\partial{\mathscr{L}}}{\partial(\partial_{\mu}A_\nu)}=(\partial_\rho A^\rho)\eta^{\mu\nu}$$ ...
1
vote
0answers
51 views

Partial derivative vs Total derivative

This is essentially a follow up to my question here since I seem to have some difficulties regarding the differences between partial and total derivatives. Consider a Lagrangian density ...
3
votes
2answers
230 views

Tensor index notation with e.g. square brackets

I want to learn playing with indices and some notation in General relativity. But in every book just is used this notation. I know upper and lower but I don"t know the meaning of some combination of ...
0
votes
2answers
49 views

Can you set all dummy indices equal to each other? [closed]

According to the Einstein summation convention, can you set all dummy indices within a same expression equal to each other? Example, if both α and β are dummy indices in a same expression can you set ...
1
vote
3answers
67 views

What is the $ds^2$ notation in relativistic physics?

Could someone please explain me intuitively how $ds^2$ represents distance in relativistic physics?
0
votes
1answer
53 views

Using the Metric in Book Gravitation (MTW)

Here is the whole Box 2.2, at Page 55 The dot behind the second $-p^2$ seems to be a "planck mass" (sarcasm, flea egg) or just the book's style to use Dot behind the equations. So the Equation is ...
0
votes
2answers
31 views

Sig Figs, Combined Operations

Using the sig fig rule for addition / subtraction seems to break in certain circumstances. For example (I'm using underlines to show sig figs): $\underline{66}+\underline{66}-\underline{1.3}\times ...
0
votes
0answers
70 views

Need some help understanding Relativistic Notation

My question originates from what is done in the book on Quantum Field Theory book by Mark Srednicki on page 21 (if anyone has it). So say you have an inertial frame that is represented in the ...
0
votes
2answers
107 views

Derivation of Schrodinger's wave equation

To derive $$i \hbar \frac{\partial}{\partial t} \psi = H \psi,$$ we start with $$i \hbar \frac{\partial}{\partial t} |\alpha \rangle = H| \alpha \rangle$$ and then multiply by $\langle x|$ on the ...
3
votes
1answer
97 views

Working with indices of tensors in special relativity

I'm trying to understand tensor notation and working with indices in special relativity. I use a book for this purpose in which $\eta_{\mu\nu}=\eta^{\mu\nu}$ is used for the metric tensor and a vector ...
5
votes
1answer
81 views

Meaning of integral signs in classical physics

When I began studying physics, by myself, on a universitary textbook, F.J. Keller, W.E. Gettys , M.J. Skove, Physics, about one year ago, I believed that all the integrals that I was going to find in ...
2
votes
1answer
33 views

Question about the expression of Witten Index

I am studying supersymmetry by myself. I do not understand the expression of Witten index, which is ${\rm Tr}(-1)^{F}$. What does it mean by writing $-1$ to the power of an operator $F$? Is this ...
1
vote
1answer
117 views

What does $L^2(S^1,\mu_H)$ mean?

It's a Hilbert space, $\mu_H$ stands for the Haar measure on $U(1)$, but what does $S^1$ mean? I found it in one of my quantum mechanics books which approaches from a very 'mathematical' way.
1
vote
4answers
57 views

Same equation, different meanings

I went into a physics classroom today and saw this equation written on the board: $$ E = \frac \sigma \epsilon $$ At first I thought it referred to the electric field $ E $ between 2 parallel plates ...
1
vote
2answers
35 views

Notation of complex valued atomic orbitals

Atomic orbitals are usually labeled $1s$, $2p_x$, $2p_x$, $2p_z$ and so on. These wave functions are defined to be real valued. The original wave functions are complex valued. The $2p_x$ orbital is ...
3
votes
2answers
67 views

Computational advantages of various notations for electromagnetism [closed]

Most undergraduate electromagnetism classes and textbooks use vector notation to describe Maxwell's equations. However, there are other notations like differential geometry and geometric calculus ...
1
vote
0answers
34 views

Basic Vector field question about notation [closed]

I am taking my first class in electrodynamics and the problem I am working on has a notation I have never seen before Consider a vector field of the form $V= f(x)y + g(y)x$ Is this essentially the ...
1
vote
3answers
136 views

Physical Explanation of Quantum Mechanics Notation? [closed]

CLARIFICATION: I just don't understand what the notations below mean and how to use them. ============= I just started taking QM, and the new notation is quite confusing. While the math makes a ...