Styg
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Optical theorem in QFT
Accepted answer
6 votes

You might be assuming the matrix element $T_{ii}$ to be real. If so, then $$ \lvert S_{ii} \rvert^2 = 1 + \lvert T_{ii} \rvert^2 > 1 $$ Without such an assumption, $$ \begin{align*} \lvert S_{ii} ...

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Is the partial trace of a mixed state always mixed? If not, are there natural examples where the partial trace of a mixed state is a pure state?
4 votes

Writing out Craig's answer explicitly (I personally find explicit examples helpful): $$ \rho = \frac{1}{2} \lvert 0 \rangle_{_A} \lvert 0 \rangle_{_B} \langle 0 \rvert_{_A} \langle 0 \rvert_{_B} + \...

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Derivation of time independent Schrödinger equation
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4 votes

The derivation of the time-independent Schrödinger equation doesn't assume both sides equal a constant. It begins with the assumption that the wavefunction can be written as a product of two functions:...

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What is the difference between generalized momentum and ordinary momentum?
Accepted answer
2 votes

They're (in principle) different quantities, that coincide for velocity-independent potentials in a Cartesian coordinate system. The Lagrangian and the generalized momenta in such a system are $$ \...

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Would a string vibrating in an atmosphere that is different from Earth's have a different overtone series?
1 votes

No interaction with an external environment is assumed when deriving the allowed frequencies for a string. The basic assumptions are that tension is the same at every point on the string, and that ...

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How can Hydrogen show spectrum with only one orbital?
1 votes

The Bohr model does not limit the number of possible orbitals that hydrogen has. At any given time, the single electron is in any one of the possible orbits, sure. But there is no restriction on which ...

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How to express random spin up / spin down particle or beam in spin z basis?
1 votes

What you're looking for is a density operator. Writing a quantum state as a Dirac state $\lvert \psi \rangle $ implies a well-defined state, that is, that there is a set of Hermitian operators with ...

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Electric field of a parallel plate capacitor in different geometries
1 votes

We do take into account the field due to both plates in the cylindrical geometry. The field due to an infinite uniformly charged cylinder is zero in the interior of the cylinder, as can be shown by ...

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If we move from one point to another with constant speed/velocity will the work done be zero or not?
Accepted answer
1 votes

You're right in saying that the work performed on an object with constant velocity is 0. The work-energy theorem says that the net work done on an object equals change in its kinetic energy. $$ W_{net}...

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Work done in moving a charge
0 votes

The work energy theorem says that the net work done on a point mass equals the change in kinetic energy. $$ \int \vec F_{net} \cdot d\vec r = \frac{1}{2} m \Delta (v^2) $$ In the hypothetical ...

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Central Force Motion
0 votes

It might be better to not think of $\frac{mv^2}{r}$ as the expression for centripetal force, and instead to think of $\frac{v^2}{r}$ as the acceleration of a particle moving in a circle of radius $r$ ...

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Intensity of electric field and electric potential
0 votes

If you are beginning with electrostatics, you must have been introduced to Coulomb's Law for force between two point charges $q_1$ and $q_2$: $$ F \propto \frac{q_1 q_2}{r^2} $$ where $r$ is the ...

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Linking Gravitational Field Strength and Gravitational Potential confusion
0 votes

Post the discussion in comments, here is my answer: It is not correct to say that $g = -\frac{\partial V}{\partial r}$, where $g$ is the magnitude of the gravitational field. The full statement for a ...

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Confusion regarding EMF definition
0 votes

The emf as defined between two electrodes is the difference in electric potential $V$ between the two electrodes. If $A$ and $B$ denote the locations of the two electrodes, then emf can be defined as ...

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Change of mass change in velocity
0 votes

As Chris mentioned in his comment, it depends on how the mass is lost. Specifically, it depends on the velocity of the mass that is lost. I'm assuming that the entire system, consisting initially of ...

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Forces in lagrangian mechanics
0 votes

You would have to include the tension as a generalized force if you did away with the constraint that $r$ is constant when writing your Lagrangian (since it acts inward towards the support, that is, ...

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Electric potential at earth and infinity
0 votes

Short answer: measurements would not change if the earth is taken to be at $100V$ instead of $0V$. The physically measurable quantity in electrostatics is the electric field, derived from the ...

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What force creates the contact/normal force?
0 votes

There are two possible interpretations of the question: What is the microscopic origin of the normal force? If we accept the existence of contact forces, why would the rolling drum apply a normal ...

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What's happening when $V = I$ ($R$ equals one)?
-1 votes

To add on to Billy's answer, there is no deeper meaning because $R$ is not dimensionless. Let's take $R = 1\Omega$ for the rest of the answer. Let upright letters denote numerical values of the ...

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