# Tag Info

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A fermion is any particle, elementary or composite, that obeys Fermi-Dirac (as opposed to Bose-Einstein) statistics relating to how identical particles behave when you swap two of them. Due to an important but complicated result, this is taken to amount to having half-integer spin. A lepton is one type of elementary particle with spin 1/2. The only leptons ...

12

First, you have system with some energy, named $U$ by physicists. You think you have all the information you need to characterize the system but then some guy comes near and says: "Whoa, that's bad, the volume of your system can change." You say: "No problem, we just add here $pV$. Our new energy is $H=U+pV$." "But hey," they say, "your temperature can ...

9

Short answer: Gibbs free energy $G = U + PV - TS$ combines internal energy $U$, pressure $P$, volume $V$, temperature $T$, and entropy $S$ into a single quantity that measures spontaneity. With that, I mean that processes that lower the Gibbs free energy of your system will spontaneously occur, and equilibrium is reached when the Gibbs free energy reaches ...

9

A fermion is any particle characterized by Fermi–Dirac statistics and obeying the Pauli exclusion principle. So for example quarks are fermions, as are Helium-3 atoms. A fermion does not have to be an elementary particle. I'm not even sure that it has to be spin $\tfrac{1}{2}$, though I can't think of any fermions that aren't. A lepton is a spin ...

5

Sanaris's answer is a great, succinct list of what each term in the free energy expression stands for: I'm going to concentrate on the $T\,S$ term (which you likely find the most mysterious) and hopefully give a little more physical intuition. Let's also think of a chemical or other reaction, so that we can concretely talk about a system changing and thus ...

4

It is a "crank and slider" or "slider-crank" mechanism.

4

The Standard Model includes 12 elementary known as fermions that respect the Pauli exclusion principle. They include six quarks (up, down, charm, strange, top, bottom), and six leptons (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino) (ref) All leptons are fermions, but not all fermions are leptons.

4

The word 'Physics' comes from the Greek Word for 'Nature' (written as 'φύση'). From Google: 'etymology of physics' physics - ˈfɪzɪks noun: physics the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics includes mechanics, heat, light and other radiation, sound, electricity, magnetism, ...

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The other answers are correct. I would like to add to them with an example. Take a spring, with spring constank $k$, with a mass, $m$, at one end and fixed to a large immovable object at the other. Let the only force acting on the mass be due to the spring and the difference from the equilibrium position to be $x$, which can be positive and negative. This ...

3

The equation you gave is indeed the definition of matrix multiplication, applied to a $d\times d$ matrix and a $d\times 1$ matrix. But the underlying concept is something more. The thing about vectors is that they exist, in some sense, independent of the numbers used to represent them. For example, an ordinary 3D displacement vector represents a physical ...

2

Both $h$ and $\tilde{h}$ are usually called weights. Their sum, $\Delta=h+\tilde{h}$ is the (scaling) dimension of the operator, while the difference, $s=h-\tilde{h}$ is called the spin. This is due to their association with scale transformations (dilatations) and rotations, respectively. To see this, note that the dilatation operator is given by ...

2

Torque is not a force. You can say there is a torque caused by normal forces, but there is no special name for that. A normal force comes from acting with a force on an object resting next to a surface. The surface prevents the object from moving through it by producing a reaction force that is necessarily normal (perpendicular) to the surface (parallel ...

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There are two forces inluencing the spontaneity of a reaction: (1)The tendency of a system to attain a state of minimum energy and maximum orderedness, or stability. (2)The tendency of a system to attain a state of maximum energy and minimum orderedness , or entropy. If a system attains maximum stability, it attains mininum entropy; and if it attains ...

2

If you have different Hilbert spaces, you cannot say it is the same operator on them, since operators are defined on the Hilbert space. The momentum operator is a tricky one for many systems, and rigor requires the discussion of concepts like rigged Hilbert spaces. A nice introductory discussion of this is "Mathematical surprises and Dirac's formalism in ...

2

In the simplest sense of it, the Free Energy is the heat of the system minus the compulsory heat loss due to entropy. So, in short, it is the amount of "energy" left over in the system, after we consider losses due to entropy. So basically some amount of heat is wasted, and the remaining amount is useful. And this remaining amount is the Gibbs Free Energy. ...

2

A multi-body problem consisting of $N$ objects requires $N$ coupled differential equations that need to be solved simultaneously (if you want to find the objects trajectories in time with known initial positions) When you solve $x + 2y = 3 \text{and} x + y = 2$, this is what is known as mathematical analysis. The exact solution can be found: $$x = 1, y = ... 2 The eigenvalue is something physicists should be familiar with. For some matrix, A, multiplied by some vector \mathbf x, we get$$ A\mathbf x=\lambda\mathbf x \tag{1}  where $\lambda$ is the eigenvalue, a characteristic of $A$ on $\mathbf x$. An eigenfunction is related to Equation (1). Given an operator (a differential operator in the case of quantum ...

2

An electromagnet is an electromagnet. i.e.: a (insulated) wire wrapped around an iron core that produces an electromagnetic field when current is passed through it. A solonoid uses an electromagnet to perform a mechanical function.

1

Acceleration is simply a rate of change of velocity. So the magnitude tells you, how quickly velocity changes.

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This is a usual term about solving differential equations. By "analytic" (or mathematical analysis), we mean finding an algebraic expression like $y=f(t)$ which satisfy the desired differential equation. But sometimes we solve the equation only at some special points. The latter method is called "numerical". Since the Newton's law (and other principal ...

1

In quantum chemistry two-center integrals refer to exchange or coulomb integrals involving 1-electron atomic wave functions (orbitals) centered on two different atoms in a molecule. Say the coulomb repulsion between an electron described by an orbital belonging to atom A and another electron described by orbital belonging to atom B is given in a simplified ...

1

If you were looking at a real person, as you move, their images changes: from the left, you see their left side image, from the right, you see their right-side image. This phenomenon is call parallax, and is partly responsible (in addition to binocular vision), for depth perception. In monocular vision, parallax is the only cue. In a painting, there is ...

1

The name you're looking for is ubiquitous gaze, or also pursuing eyes. This is an optical illusion (which means that it is exclusively a function of how our brain interprets its visual inputs) and it can be realized on completely flat canvas by appropriate handling of perspective. For more information see e.g. this HowStuffWorks page.

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A fermion is just a particle of half-integer spin. Being a lepton for a particle is a matter of definition of global symmetries of the theory. This means that a lepton can in principle be both a fermion or a boson, although all known leptons are fermions (electron, muon, tau and their neutrinos). One example of bosonic lepton is the weak triplet Higgs ...

1

This is d'Alembert's principle. The basic, very general idea is to take Newton's second law applied to an accelerating mass, and write it as $F-ma=0$. That is, we take the $ma$ term and pretend it's another force balancing the $F$ term. This allows us to think about the dynamic, accelerating mass as if it's a static system. The $ma$ term is what's referred ...

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is a thermodynamic potential that measures the "usefulness" or process-initiating work obtainable from a thermodynamic system at a constant temperature and pressure (isothermal, isobaric). Just as in mechanics, where potential energy is defined as capacity to do work, similarly different potentials have different meanings. The Gibbs free energy is the ...

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Astronomy talks about celestial objects (such as stars, galaxies, nebulae etc) and celestial phenomena (such as gamma ray bursts etc), their position, motion, evolution, chemistry, physics. Astrophysics is a sub-branch of astronomy to deal with physics of celestial objects and phenomena. The first encounter: A guy put microscope in front of rainbow spectrum ...

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Richard Feynman has nice words about science. It is not bad to read chapter 3 of "Feynman Lectures on Physics". The main point of his lecture is that "there is no strict boundary between different fields of science", "nature doesn't concern what we call its parts!" So, we can't look for a line that divides celestial works into astronomical or astrophysical ...

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