Questions tagged [superposition]

A basic principle of solutions of *linear* differential (often wave) equations, ensuring that the sum ("superposition") of two solutions is automatically a solution as well. Conversely, solutions (amounting to quantum states in quantum mechanics, since the Schrödinger equation is linear) can be represented as a sum of two or more other distinct solutions, and so can be Fourier/eigenstate resolved to enhance mathematical tractability.

Filter by
Sorted by
Tagged with
0
votes
1answer
22 views

Electric field inside spherical cavity charge density

If there is a non-conducting solid sphere with uniform volume charge density $\rho$ and inside it there is a spherical cavity located outside the center of the sphere, why is it the case that the ...
1
vote
2answers
29 views

Standing waves - why do wavelengths fit perfectly?

When reading about standing waves it is always said that only certain wavelengths are "allowed". I understand that these wavelengths are a requirement for there to be a standing wave due to ...
0
votes
1answer
27 views

Why can't we add up energy of 2 progressive waves to find the energy carried by a stationary wave?

with displacement as the y axis and distance along wave as the x axis, let's say that the first progressive wave has an amplitude of y and a displacement of y at distance x and the second progressive ...
0
votes
0answers
44 views

Is spacetime entangled with a free particle?

Consider a single free particle. If a spacetime metric satisfies the superposition principle, then the full state of the particle and the spacetime should be $$\sum w_{x,y,z,t}|x,y,z,t\rangle|g_{x,y,z,...
0
votes
0answers
86 views

Unequal superpositions of energy eigenstates in two-state quantum systems?

Two-state quantum systems in a superposition of energy eigenstates oscillate with time between the possible states. If both energy eigenstates contribute with the same amplitude, the oscillation is ...
10
votes
5answers
2k views

Why is Schrödinger's cat in a superposition and not a mixture if you model decay with Fermi's golden rule?

I am teaching quantum information for undergraduate math students and as a perspective I thought it would be cool for them to discuss Schrödinger's cat a bit. More precisely I'd like to come up with ...
0
votes
1answer
22 views

AC circuit and Superposition Theorem

I want to find $\Delta V_{ab}$ for the circuit on the figure I have tried to use the superposition theorem, and then Here I find my first question, because if there is a coil between A and B, then $\...
1
vote
3answers
43 views

Why do we hear beats?

I've learnt quite recently that to hear beats the sources must emit sound in almost near frequencies Here is a scenario I have a two tunning forks and together the produce a beats of frequency 2hz But ...
2
votes
1answer
33 views

What happens if a string with both ends fixed is excited with sinusoidal wave with $\lambda \neq 2 L/n $?

We know that if $\lambda = \frac {2L}{n}$ then stationary waves are formed. So, if a wave generator is connected to the string and we set $\lambda = 2L $ then we will see stationary waves. Maybe we ...
-1
votes
0answers
29 views

Is Perseverance Rover in a superposition of crashed and not-crashed?

I’m trying to understand superposition. I’m aware of Schroedinger’s cat, and not knowing. What I’m interested in is our inability to know, for example if the event happened more recently than the ...
0
votes
2answers
56 views

Superposition of two electromagnetic waves [closed]

Suppose two EM waves (same frequency) polarized perpendicular to a plane $\mathbb{\sigma}$ are travelling along $\overrightarrow{k_1}$ and $\overrightarrow{k_2}$ and they meet at some point say $P$. ...
0
votes
0answers
51 views

the measurement problem, what is it that drives the wave function to collapse?

I'm hearing a lot of different solutions to the measurement problem. But what is the right answer? Does consciousness play a role in the collapse of the wave function or is there a different factor at ...
0
votes
1answer
20 views

Induced electric field and electric field due to charges obey superposition?

Say a group of charges and a varying magnetic field exists in some region. We'll have two electric fields,due to the charges and due to the magnetic induction. Does the total electric field equal the ...
1
vote
1answer
73 views

How are linear combination of energy eigenstates solutions to the TISE?

My textbook states that: TISE is a generic eigenvalue problem and the superposition state is not a solution to the TISE. Another part of textbook (in context of infinite square well): The most ...
0
votes
0answers
22 views

Group Velocity Clarification

There is something that confuses me a bit about how group velocity is sometimes introduced and explained. For example, Walter Lewin (great professor) in his lectures uploaded on youtube, explains the ...
1
vote
2answers
99 views

Atom in superposition: is it an atom-photon system, and what is the role of the environment?

Let's assume an atom would get from its ground state $|g\rangle$ to its first excited state $|e\rangle$ by absorbing a single photon. Now, let's assume the atom gets from $|g\rangle$ to $\frac{1}{\...
1
vote
3answers
67 views

Can unitary evolution produce a superposition of wavefunctions, or do wave functions have to be 'created' in a superposition before evolution?

A quantum superposition is a wave function such as : $$ |\psi\rangle = \alpha |\psi_1\rangle + \beta |\psi_2 \rangle $$ Unitary evolution will transfer these states to $|\psi'\rangle \to U|\psi\...
0
votes
1answer
50 views

Is it physically meaningful to combine a photon's position state space with its polarization state space?

Mathematically, we can take the tensor product of a photon's position state space $\mathscr{H}_{pos}$ with that of its polarization state space $\mathscr{H}_{pol}$. Then, in the resulting Hilbert ...
0
votes
0answers
49 views

Does Lagrangian follow superposition principle?

In other words: is the Lagrangian of a composite system the sum of the Lagrangians of its components? It shouldn't be, since it's energy. But then we lost one of the most important principles in ...
0
votes
2answers
61 views

What is the physical meaning of multiplication of two wavefunctions?

In the amount of quantum mechanics I'vs learnt I understand what wave functions are, how do we extract information from them and so on, and that addition of two wavefunctions on renormalization gives ...
0
votes
2answers
97 views

Proof of A superposition of stationary states is not a stationary state

This is proof: (Is the superposition of stationary states a stationary state? If not, then why not?) A superposition of stationary states is not a stationary state. Suppose we have two kets, $| E_1 \...
1
vote
1answer
76 views

What does this quantum mechanics diagram about adaptive mutations mean? [closed]

I'm a current high school student and I’m aspiring to become a biochemist. I’m at the moment writing an article about adaptive mutations but there is a lot of tricky quantum mechanics in it which I ...
0
votes
1answer
18 views

Why two vibrations of different frequencies and amplitudes need to be commensurable when the resultant vibration is formed from their superposition?

I was reading chapter 2 of AP French's Vibrations and Waves. In the section "Superposed Vibrations of Different Frequency, Beats", this paragraph confused me :- "Unless there is some ...
0
votes
2answers
69 views

Position matrix representation in QM [closed]

For quantum harmonic oscillator, if wave function is in a superposition of two wave functions, $$ \psi(x)=(1/\sqrt2)\psi_n(x)+(1/\sqrt2)\psi_m(x) $$ and position operator is represented as a matrix, ...
3
votes
2answers
128 views

Is there a superposition of two density matrices?

Say I have two density matrices $\rho_0 = \sum_{i,j} \alpha_{i,j} |i\rangle \langle j|$ and $\rho_1 = \sum_{i,j} \beta_{i,j} |i\rangle \langle j|$. What is the density matrix $\rho$ corresponding to ...
1
vote
2answers
58 views

Amplitude, constructive and destructive interference in the real world, in quantum waves

A light bulb puts out a stream of photons with various wave amplitudes. If we add more light bulbs in the room, how can we just assume that the light intensity increases to greater levels; that ...
4
votes
1answer
89 views

Easiest way to see that superposition is necessary?

I have been discussing QM with a friend and wanted to explain why holding on to realism means we must accept non-locality. Essentially I got hung up on explaining Bell's Theorem in simple words. I ...
9
votes
3answers
204 views

How can photons destructively interfere?

This is a concept I don't fully understand. If I have two photons each with frequency $\nu$, then they each have an energy of $E = h\nu$. If they get matched with an inverted phase, then the summed ...
0
votes
1answer
37 views

Superposition Principle and Forces

Why does Griffiths write in his book - "For not only does the force on test charge $Q$ depend on the separation distance $r$ between the charges, it also depends on both their velocities and on ...
0
votes
1answer
25 views

Ferromagnetic field near a ring in Earth's magnetic field

Let's say I am trying to find out the effect that an iron ring has on the Earth's magnetic field (approximated to a uniform field at infinity). Can I solve it in 4 steps: Find the magnetic field due ...
1
vote
1answer
53 views

Superposition of states in second quantization

Suppose I have a particle of unspecified spin whose states are determined by a single quantum number $k=1,...,N$. In standard quantum mechanics notation, the state such that the particle is in a ...
-1
votes
1answer
65 views

Why is the phase difference an “odd number of half-wavelengths” when two waves interfere destructively? [duplicate]

Excerpt from the Feynman Lectures, Volume III, Quantum Behavior (emphasis mine): At those places where the two waves arrive at the detector with a phase difference of π (where they are "out of ...
0
votes
2answers
61 views

Are two waves out of phase only when the phase difference is $\pi$?

Excerpt from the Feynman Lectures, Volume III, Quantum Behavior: At those places where the two waves arrive at the detector with a phase difference of $\pi$ (where they are “out of phase”) the ...
3
votes
2answers
109 views

Where does the energy vanish in wave interference? [duplicate]

In my physics textbook there is a chapter on waves. Now there is a topic on interference. I don't understand why I get additional energy there. Suppose two waves presented as $Y_1=3\sin(\omega t)$ and ...
0
votes
3answers
39 views

Why are only some eigenstates observed upon collapse?

If we have a system in a superposition of states, we expect that observation would collapse the wave-function to one state. But many eigenstates can be expressed as a superposition of other ...
0
votes
0answers
30 views

Zero energy for two opposite traveling waves

Is it possible for two waves travelling the opposite way on a rope of some finite length $L$ (connected to two infinite ropes on the edges) to have a total of zero energy? For example, if we look at: $...
0
votes
0answers
32 views

Should we think about superposition in a fuzzy or in a paraconsistent manner?

Suppose we define a predicate $L$ as "is alive." We then take Schrödinger's cat, $c$, and put it in its box and wait for a time for it to be equally likely for it to be dead and alive. How ...
0
votes
2answers
40 views

Energy of photon from superposition to ground state

Let an atom is in superposition of two eigen energy states E1 and E2. If it returns to the ground level E0 what energy should have the photon released in the process?
0
votes
1answer
30 views

Energy of spin in Stern Gerlach

Consider a Stern Gerlach devise. If the spin of the Ag atom makes an angle of say 30 grades according the magnet's up direction would Ag come out in the up or down ray on the plate behind? I consider ...
3
votes
2answers
71 views

Do vectors imply the superposition principle?

I don't understand why it is necessary to state the superposition principle. Reading Griffiths' Introduction to electrodynamics, the superposition principle is described as experimental fact that is ...
0
votes
1answer
25 views

After taking measurement of a particle in superposition states does it collapse

I have this question: A particle is trapped inside an infinite square well of width L, this particle is in a superposition state n=1 and n=3 such that : $\psi(x)=\sqrt{2/5}\psi_1(x)+\sqrt{3/5}\psi_3(x)...
0
votes
0answers
64 views

The structure of Worlds in Many Worlds theory

I've read David Deutsch's article where he explains - in terms of information flows - how different Worlds can be located in the same 3D space (as we perceive it) while do not interact with each other....
0
votes
1answer
39 views

Standing waves on string

I am a high school student and I am a little confused about standing waves on string, My confusion is that: we know ,A standing wave is formed by the interference of reflected wave and incident wave ...
1
vote
1answer
86 views

Why are Superposition states not solution of TISE?

Form a textbook i am learning for its says: All valid wave functions (energy eigenfunction with definite energy and superposition states with simultaneously multiple energies) for a given quantum ...
0
votes
0answers
98 views

What are fundamental reasons for conservation laws in Quantum Mechanics?

Let me be a little silly and suppose that when "God" created our Universe - he had these 3 options: (Most classical): let the energy (contained in any particle = field excitation) spread ...
-1
votes
1answer
25 views

What is the Main contrast between classical coin toss and superposition state?

We know that in normal coin-toss there is two probable states HEAD OR TAIL. When we commence for measuring only get head or tail,is it means two probable states collapse into one {H or T}.in ...
0
votes
1answer
54 views

If we assume that principle of quantum superposition is wrong, would this invalidate Alain Aspect experiment? [closed]

If we assume that principle of quantum superposition would be actually not true, would this invalidate conclusion from the Alain Aspect experiment that there is no local hidden variable?
4
votes
6answers
193 views

Why don't photons interfere/interact with one another, as common mechanical waves would?

After all, they are a (self-sustaining) perturbation of the same field, like sound waves or water waves are "energy flow" (except these ones experience dissipation). And how can our eyes be ...
1
vote
3answers
249 views

Why is the effect of Coulomb's force the same on more than two charges?

As we have developed the idea of electric field lines from Coulomb's law. If two equal and opposite charges are in plane, all the effect of electric field vectors adds to line joining the two points, ...
1
vote
1answer
70 views

Confusion between superposition of SHMs

I am a high school student and i am little confused between superposition of Simple harmonic motions{SHM's}, suppose a spring of spring constant $k_1$ has time period $T_1$ and another spring of ...

1
2 3 4 5
14