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10 votes

Physical meaning of each term of the square modulus of a wave function

1 - The cross term $\psi_0\psi_1\cos(\omega t)$ can be interpreted as an interference term of the states $\psi_0$ and $\psi_0$, which importantly depends on time, as these states have different ...
Gabriel Ybarra Marcaida's user avatar
4 votes

Strange calculus involved in work and power

The correct formula for work is $$ \Delta W = \int P d t = \int \vec{F} \cdot \vec{v} \,dt $$ Now, if $\vec{F}$ is constant, then we can take it out of the integral and write $$ \Delta W = \vec{F} \...
Prahar's user avatar
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4 votes
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Problem Deriving "The General Uncertainty Principle" in Section 5.7 of Susskind's "Quantum Mechanics"

You are correct, but there's one last simplifying step. The norm of the product is the product of the norms. For two complex numbers, $z_1$ and $z_2$: \begin{equation} |z_1\cdot z_2| = |z_1|\cdot|z_2| ...
Aiden's user avatar
  • 1,900
4 votes

I need to find the state of the system at a general time, knowing the Hamiltonian and the state at $t=0$

For this particular initial state, you do not need to diagonalize the Hamiltonian. The reason is that this particular initial state is an eigenstate of the Hamiltonian, and as a consequence you can ...
Níckolas Alves's user avatar
3 votes
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Is the answer given in the option wrong?

The answer sheet is correct. You are ignoring the statement “The direction of the motion of the object changed only once, at time t.” That means that the velocity was zero at time t. So before time t ...
Dale's user avatar
  • 103k
3 votes

Can you ever obtain a pure rotation from composing Lorentz transformations?

Ever? Always, of course, for infinitesimal boosts. Review your Wigner rotations but consider the evidently superior 2$\times$2 matrix representation of the spinor map, which protects you from the busy ...
Cosmas Zachos's user avatar
2 votes
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Buoyancy basics

The intuitive way to think about these types of buoyancy problems is in terms of the pressure due the heads of the fluids. Starting with the stated set up, the pressure under the ice cube due to the ...
KDP's user avatar
  • 6,142
2 votes
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How to expand $(D_\mu\Phi)^\dagger(D^\mu\Phi)$ in $SU(2)$?

You appear to not appreciate your expression as a row vector dotted on a column vector (possibly sandwiching operators). I corrected your expression to $$\partial_\mu\Phi^\dagger \partial^\mu \Phi - \...
Cosmas Zachos's user avatar
2 votes

What does $v$ actually represent in pulley problems?

By your definition that $v=dl/dt$, $v$ is just the rate of change in the lengths of the rope segments supporting their respective masses. Here you define $v$ to be a scalar, since $l$ is also a scalar,...
hendlim's user avatar
  • 692
2 votes
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Question regarding gravitational force as external force

My doubt is if gravitational force is considered as an external force Yes, it is considered as an external force, an external conservative force. ...so how come can we apply Total mechanical energy ...
hft's user avatar
  • 21.9k
2 votes

Issue with simplifying the equation related to non-uniform acceleration

The equation $$ \frac {d v}{dt}= A+ B\, v^2 $$ with constant $A$ and $B$ is an example of a Riccati equation. The Wikipedi article shows you how to solve it.
mike stone's user avatar
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2 votes

For an objective falling, reaching terminal velocity and then hitting the ground, how can I find the force it exerts on the ground?

Short answer: The given information is not enough. Long answer: You correctly noted that the force of the impact is related to the change in momentum. We take off from there. If we assume the duration ...
Saeed's user avatar
  • 216
2 votes
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Doubts in circuit analysis

Maybe I am loosing some detail here, but assuming that all resistances are equal, and looking at the symmetry of the circuit, all dpps and currents should be the same in module if you flip the circuit ...
ebenezer's user avatar
  • 130
1 vote

Buoyancy basics

Divide the world into 3 parts. 1) The ice cube, 2) the fluid, and 3) enough fluid to fill the hole if the ice cube was not there. If you only had 1) or 3), they would fall down because of their weight....
mmesser314's user avatar
  • 41.1k
1 vote

1D Lattice with site dependent magnetic field

I would say the result is just a statement about the structure of the phase/configuration space, which is spherical with no preferred direction(s) in the case of a magnetic moment. The partition ...
Crisco's user avatar
  • 95
1 vote
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A capacitor partially filled with dielectric

For some background, let's remind ourselves that the electric field is a conservative field. Because of this, we can define potentials that are independent of the particular path of integration. So ...
David's user avatar
  • 2,697
1 vote
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Rotating a system

As for what most people mean when they say rotate the axis - yes, it usually implies keeping all objects in the same points in space, and just using new coordinates to express their position, velocity ...
Ido's user avatar
  • 26
1 vote

Strain energy stored in a bungee cord pulled at its midpoint

When a spring is halved, its spring constant $k$ is doubled. Because I'm treating this as a two spring system I need to double the value of $k$ that I'm using. Using a value of $k=280$ N/m gives $x=....
Imperator's user avatar
1 vote
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Buoyant force on a stick making an angle theta with the vessel

Divide the underwater world into two parts - the water and the stick. Suppose the water disappeared, leaving the stick. The force on the stick would be the weight of the stick. Suppose you replaced ...
mmesser314's user avatar
  • 41.1k
1 vote
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How to calculate the relative speed when three bodies are involved?

Just draw a principal vector diagram of separate movements : Add $\vec B + \vec C = \vec C~'$ and you will get woman velocity relative to the ground. Now subtract that from train's A velocity vector ...
Agnius Vasiliauskas's user avatar
1 vote

Complex Conjugate of Wave Function's Derivative

Basically it goes like this : $$\begin{align} \left( \frac{i\hbar}{2m} \frac{\partial^2 \Psi}{\partial x^2} - \frac{i}{\hbar}V\Psi \right )^* &=\\ \left( \frac{i\hbar}{2m} \frac{\partial^2 \Psi}{...
Agnius Vasiliauskas's user avatar
1 vote
Accepted

Electrostatic potential outside of a charged ball

Starting from the general form of the electrostatic equations $$\begin{align}\mathbf{\nabla} \times\mathbf{E}(\mathbf{r})&=0 \tag{1} \label{1}, \\[5pt] \mathbf{\nabla} \cdot\mathbf{E}(\mathbf{r})&...
Hyperon's user avatar
  • 6,744
1 vote

Deriving the equal time anti-commutator of the Dirac fields

The relation you are trying to show is wrong. The equal-time anti-commutation relations for the Dirac field are (see for example Peskin & Schroeder, (3.108) ) \begin{align} \big\lbrace\psi_a(\...
Mateo's user avatar
  • 426
1 vote
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Forces accelerating a tire

I suggest a simple model to cover the no slipping and the slipping situation. Why don't the green and blue arrows simply cancel out, resulting in no acceleration/motion? Because the forces act on ...
Farcher's user avatar
  • 97.9k
1 vote
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Spherical pendulum newtonian

If you have no initial velocity perpendicular to the plane of your picture you will not have motion in phi direction, only just a normal pendulum, so you have to give it a push in phi direction at the ...
trula's user avatar
  • 6,362
1 vote

$z$-component of electric field due to a static square loop

The electric field at a point P located at a distance $z$ above the center of a square, due to only one side of the loop is given by, \begin{equation} \mathbf{E}(P)=\frac{\lambda}{4\pi\epsilon_0}\int_{...
MauvaiseFoi's user avatar
1 vote

Maximizing proper time with parabolic trajectory in uniform gravitational field

The uniform gravitational field is oriented in the $-z$-direction, with acceleration $g$. Clock A is at rest at $z=0$ and reads time $t_A$. Clock B is allowed to move in three-dimensional space $(x, y,...
Aiden's user avatar
  • 1,900
1 vote

I need to find the state of the system at a general time, knowing the Hamiltonian and the state at $t=0$

The Hamiltonian for a certain three-level system is represented by the matrix $$H = \begin{pmatrix}a & 0 & b \\ 0 & c & 0 \\ b & 0 & a\end{pmatrix},$$ where $a$, $b$, and $c$ ...
hft's user avatar
  • 21.9k

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