i recently read about the stern-gerlach experiment and found out that they did it in the first place to verify the principle of the "space quantization " introduced by Bohr , and they thought they did detect the quantization of the orbital angular momentum of ( L = 1 , m = 1,-1 ) neglecting the...
I'm just starting my undergraduate Quantum Mechanics course. I had a homework problem to show that \Delta S_x = \sqrt{\langle S_x^2 \rangle - \langle S_x \rangle ^2} = 0 , S_x being the spin in the x direction. I managed to solve it, but the physical interpretation is confusing me. If I...
I was thinking to myself, how come are particles coming from the sun gets deflected the way they do due to earth's magnetic field?
They are getting pulled toward the poles, but if we think in terms of classical Lorentz force, they should not just follow the magnetic field lines, but rather start...
Practically it is said that, given two spin states |u⟩ (up) and |d⟩ (down) - which are the spin measured along the +z and -z semiaxes - such that they are orthogonal ( ⟨u|d⟩ = ⟨d|u⟩ = 0), it is possible to write any other spin states using a linear combination of these two (because they are a...
After computind dirac 1D equation time dependant for a free particle particle I get 2 matrixs. From both,them I extract:
1) the probablity matrix P =ps1 * ps1 + psi2 *psi2
2) the current matrix J = np.conj(psi1)*psi2+np.conj(psi2)*psi1
I think that current is related to electricity, and...
I derive the quadratic form of Dirac equation as follows
$$\lbrace[i\not \partial-e\not A]^2-m^2\rbrace\psi=\lbrace\left( i\partial-e A\right)^2 + \frac{1}{2i} \sigma^{\mu\nu}F_{\mu \nu}-m^2\rbrace\psi=0$$
And I need to find the form of the spin dependent term to get the final expression
$$g...
In the context of non relativistic quantum mechanics, or better, if I consider the neutrino's mass to be zero, the phrase
seems to me puzzling. What I know is that if I know the direction of motion, I know the spin projection onto that direction, say ##\hat{z}##-direction. But to not violate...
Would this be an accurate portrayal of measuring the spin of an electron with a SG detector?:
The electron is in a superposition of spin-up and spin-down;
Upon entering the magnetic field of the SG detector, the electron enters a superposition of an upward trajectory and a downward trajectory...
Summary: If a measurement outcome depends on the measurement setup, is de measured not real or the measurement?
If the factual outcome of an electron-spin measurement depends on the orientation of the SG magnet, for instance up or down in one orientation and left or right in the other, does...
Hello everybody!
Let's begin with the spin. Spin of the ##\Lambda## is ##1/2## and of the pion is ##0##:
$$ \frac{1}{2} \otimes 0 = \frac{1}{2}$$
Since I know from the homework statement that ##L=1##:
$$ \textbf{J} = \textbf{spin} \otimes \textbf{L} = \frac{1}{2} \otimes 1 = \frac{1}{2} \oplus...
I will refer to the spin example outlined in the opening chapters of the Theoretical minimum.
Suppose we prepare a spin with a z component of +1. If we rotate the apparatus about 180 degrees, the ‘classical component’ of the prepared spin vector along the new axis of the detector is -1, so...
Suppose I have a system of two (possibly interacting) spins of 1/2. Then the state of each separate spin can be written as a ##\mathbb{C}^2## vector, and the spin operators are made from Pauli matrices, for instance the matrices
##\sigma_z \otimes \hat{1}## and ##\hat{1} \otimes \sigma_z##...
Let's consider Bohm's paradox (explaining as follows). A zero spin particle converts into two half-spin particles which move in the opposite directions. The parent particle had no angular momentum, so total spin of two particles is 0 implying they are in the singlet state.
Suppose we measured Sz...
We are given the wave function with spin, but it doesn't say in which Ylm each spin X± goes. So how do I know?
Examples;
(1) Ψ = 1/√3 R21(r) ( Y10
√2Y11 )
Here we have the up Spin X+ to Y10 and the X- to Y11
I notice the X- went to...
In http://www.feynmanlectures.caltech.edu/III_05.html#Ch5-S1, Feynman mentions that the 2-stage Stern-Gerlach experiment, which proves the electron spin states to be in a superposition, has never been actually done! I have also not seen any paper reporting such an experiment. My question is, has...
Let us for a moment look a field transformations of the type
$$\phi(x)\longmapsto \exp\left(\frac{1}{2}\omega_{\mu\nu}S^{\mu\nu}\right)\phi(x),$$
where ##\omega## is anti-symmetric and ##S^{\mu\nu}## satisfy the commutation relations of the Lorentz group, namely
$$\left[S_{\mu \nu}, S_{\rho...
Homework Statement
Given the expression
s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1>
obtain the matrix representations of s+/- for spin 1/2 in the usual basis of eigenstates of sz
Homework Equations
s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1>
S_{+} = \hbar...
I was reading the free will theorem and it basically says that subatomic particles and observers have to have free will because there's nothing prior to measurement that predetermines the outcome. Here's more:
The free will theorem states:
Given the axioms, if the two experimenters in question...
When a nucleus is placed inside an external magnetic field, it aligns itself parallel to the field, as that is the most stable position for it to be in. In more technical terms: it acquires an alpha spin.
When you shine radio waves at this nucleus, it absorbs energy and flips over anti-parallel...
I need a 12v DC with appropriate torque. In my design, the axle of the motor would be pointed straight in the air and I want to affix a wheel to it and have the wheel spin flat, sort of like a pottery wheel sort of design. I know what the wheel is made of, its dimensions and approximate weight...
I know that spin is a type of intrinsic angular momentum.
For electron spin is (1/2)ħ . But unit of (1/2)ħ is J.s, which is not the unit of angular momentum. Can you please explain this discrepancy?
Homework Statement
Prove that the Clebsch-Grodan coefficients (in the notation ##\langle j_1j_2m_1m_2|j_1j_2jm\rangle##) for the decomposition of the tensor product of spin ##l## and spin ##1/2## to spin ##l+1/2## are
$$\left\langle l,\frac{1}{2},m\mp \frac{1}{2}, \pm \frac{1}{2} \Bigg\vert l...
I know that total magnetic moment of an electron (I am not sure if it is magnetic moment of electron or atom, please clarify this) is sum of magnetic moment caused by orbital motion and spin angular momentum.
So,
Total magnetic moment = Orbital magnetic moment + spin magnetic moment
Do I have...
Suppose you have a pair of electrons in the same quantum state, and are thus spin entangled, and they absorb a pair of photons and release them at the same time. How would this affect the photons? Would the photons be entangled? Would it affect the photon spin, and if so, how would it affect the...
Hello, I don't understand how can electrons in triplet state can have the same value of spin? Shouldn't the spins be different because two fermions can't have the same state?
The following picture explain my question in more detail.
The figure below is from a textbook. It is explaining what excited states are using carbon as an example. I don't necessarily agree that the the state labeled as "example excited state 1" is really an excited state. Since the electrons in the 2p orbitals are unpaired, and in the absence of a...
This is about vehicle physics. I know how to calculate weight on each axle on a car during deceleration. Given the picture below:
The weight on the front axle is calculated as:
Wf=(c/L)*W-(h/L)*M*a
and the weight on the rear axle is calculated as:
Wr=(b/L)*W+(h/L)*M*a
where c and b are the...
What is the difference between parallel and antiparallel spins for a pair of nucleons?
My understanding is that nucleons have a strong tendency to pair - proton with proton, neutron with neutron, proton with neutron. When they pair their spins either:
cancel (spins pair antiparallel) pairing...