if ac travels in both directions, and pulsating dc travels in both directions, it seems that pulsating dc would just match the definition of ac, if this isnt the case then what are the differences? when would we use pulsating dc instead of ac? And how is pulsating DC made?
[Physics] What’s the difference between AC and pulsating DC
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I never have cared for the phrase a capacitor blocks DC (it doesn't) but that's beside the point here.
DC is most often used to mean a constant voltage or current rather than the original meaning of unidirectional current.
If one takes a time varying voltage and finds the time average value, this value is often called the DC component of the voltage. That is, if you subtract off the time average value (DC component) from the time varying voltage, you get the AC component(s).
This is essentially what the capacitor does here - it subtracts 2V from the 'pulsating DC' leaving only an AC voltage across the resistor. That is, if you zeroed the AC source, you would find a constant 2V - of opposite polarity of the 2V source - across the capacitor and 0V across the resistor.
The confusion arises because the word “coherent” evolved to have different meanings in different contexts where it is not fully qualified.
Going back to the 2-slit experiment, one shows that the intensity of the signal at a particular point $$ I_{tot}(x)\ne I_{1}(x)+I_{2}(x)\tag{1} $$ is not the simple sums of intensities of the signals from the two source slit. This is because the light from the slits is “coherent” in the sense that the signals can interfere at point. This website gives some details but basically the intensity at one point is of the form $$ I_{tot}(x)= (A(x)+B(x))^2\tag{2} $$ with cross-terms of the type $A(x)B(x)$ typical of interference between terms. (Despite the efforts of generations of students, $(A+B)^2\ne A^2+B^2$ so (2) CANNOT be the same as (1) in general).
This opposes incoherent light, where the intensity at a point is just the sum of individual intensities of the different sources: $I_{tot}=I_1+I_2$. This is what happens if you shine two flashlights at a wall: the intensity of the light is just the sum of the intensity from the two flashlights: there are no dark and bright fringes of interference.
Now, in a linear combination of wave functions, say $$ \psi(x) = \alpha \psi_1(x) +\beta \psi_2(x). \tag{3} $$ the various parts can, in general, interfere in the sense that the probability density \begin{align} \vert \psi(x)\vert^2 &= \vert \alpha\vert^2 \vert\psi_1(x)\vert^2+ \vert\beta\vert^2\vert\psi_2(x)\vert^2 \\ &\quad + \alpha^*\beta\psi_1(x)^*\psi_2(x) +\alpha\beta^*\psi_1(x)\psi_2(x)^* \end{align} is not just the sum of the probability densities of the individual components, i.e. it is contains cross terms of the type $$ \alpha^*\beta\psi_1(x)^*\psi_2(x)+\hbox{c.c.} $$ and is therefore reminiscent of (2). Thus we speak here of “coherent superposition”. The state of (3) is actually a pure state.
In a mixed state (which cannot be described by a wavefunction), the probability density is a sum of individual probability densities, i.e. something like $\vert\psi(x)\vert^2 =\vert\alpha \psi_1(x)\vert^2+\vert \beta\psi_2(x)\vert^2$ without the interference term. Note that $\psi_1(x)$ could itself be a sum, i.e. $\psi_1(x)=a \phi(x)+b \chi(x)$ so that $\vert\psi_1(x)\vert^2 = \vert a\phi(x)+b\chi(x)\vert^2$ can have cross-terms, but there would be no cross-terms between the pieces in $\psi_1(x)$ and $\psi_2(x)$.
Now as to coherent states. Glauber investigated the question of coherence in quantum optics, i.e. the coherence properties of the quantized electromagnetic field. The tool of choice here is the correlation function, and Glauber was able to find a linear combination of harmonic oscillator states that was “coherent to all order” in the sense of the correlation function. These states Glauber naturally called “coherent states”. Coherent states are pure states so the various parts can inteference and they are thus coherent in the sense that cross-terms appear in the probability density. However, whereas all pure states are coherent superposition of basis states, not all of them are “coherent” in the sense that their correlation functions do not satisfy the condition set out by Glauber.
To make matters worse, Peremolov realized that the Glauber coherent states could be generalized mathematically. Perelomov observed that the Glauber coherent states could be written as $$ \vert\alpha\rangle = T(\alpha)\vert 0 \tag{4} $$ where $T(\alpha)$ is displacement in the plane: $$ T(\alpha)=e^{i(\alpha a^\dagger - \alpha^* a)}\vert 0\rangle\, . $$ Perelomov used this last property to introduced “generalized coherent states”, which are just displacements of some special state (see for instance Perelomov, A. (2012). Generalized coherent states and their applications. Springer Science & Business Media.) . Hence, “spin coherent states” are defined using rotations, i.e. displacements on the sphere, by $$ \vert\theta,\phi\rangle = R_z(\phi)R_y(\theta)\vert JJ\rangle\, . \tag{5} $$ (One can also displace the $\vert J,-J\rangle$ state.)
One can show that the Glauber coherent state $\vert\alpha\rangle$ of Eq.(4) turns out to be an eigenstate of the annihilation operator $a$, i.e. $a\vert\alpha\rangle=\alpha\vert\alpha\rangle$. Obviously this cannot happen when the Hilbert space is finite dimension so angular momentum coherent states of (5) are not eigenstates of either $J_+$ or $J_-$. However, they share with many properties of the Glauber coherent states. Both sets of states have minimum uncertainty (when the angular momentum operators are properly defined), and both states produce specific factorization properties when computing some quantities. Generalized coherent states are not limited to angular momentum but have been defined for a variety of cases, either by insisting they have minimum uncertainty or they are translate of some distinguished state.
Summary: pure states are coherent superpositions of basis states. Mixed states are incoherent superpositions of states. Glauber coherent states (or harmonic oscillator coherent states) are pure states but also satisfy additional properties as laid out by Glauber in terms of correlation functions. Generalized coherent states were introduced by Perelomov; they are pure states which share some properties of the Glauber coherent states.
Best Answer
Pulsed DC current changes in value, but not in direction. It's polarity does not change. In AC the polarity constantly changes. see https://en.wikipedia.org/wiki/Pulsed_DC