What is Superposition of states: Definition and 26 Discussions

Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution.
An example of a physically observable manifestation of the wave nature of quantum systems is the interference peaks from an electron beam in a double-slit experiment. The pattern is very similar to the one obtained by diffraction of classical waves.
Another example is a quantum logical qubit state, as used in quantum information processing, which is a quantum superposition of the "basis states"




|

0
⟩


{\displaystyle |0\rangle }
and




|

1
⟩


{\displaystyle |1\rangle }
.
Here




|

0
⟩


{\displaystyle |0\rangle }
is the Dirac notation for the quantum state that will always give the result 0 when converted to classical logic by a measurement. Likewise




|

1
⟩


{\displaystyle |1\rangle }
is the state that will always convert to 1. Contrary to a classical bit that can only be in the state corresponding to 0 or the state corresponding to 1, a qubit may be in a superposition of both states. This means that the probabilities of measuring 0 or 1 for a qubit are in general neither 0.0 nor 1.0, and multiple measurements made on qubits in identical states will not always give the same result.

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  1. Yuras

    B Spectral lines and superposition of states

    Let's say atom has two energy levels, ##E_1## and ##E_2##. If atom is in the first state ##|E_1\rangle##, then it's able to absorb a photon with energy ##E_2-E_1##, while transitioning to the second state ##|E_2\rangle##. In atom's spectrum we can see an absorption line at the corresponding...
  2. E

    B Question about quantum superposition

    All of my speculation is based on my current understanding of quantum physics as an art high school student who just has this as an interest, which is in no way at a quantum physicist's level so I apologize if this question is stupid. Also sorry for my English. Most, if not all of you reading...
  3. K

    Possible Results and Probabilities of a Measurement of Operator Q

    I first Normalise the wavefunction: $$ \Psi_N = A*\Psi, \textrm{ where } A = (\frac{1}{\sum {|a_n^{'}|^{2}}})^{1/2} $$ $$ \Psi_N = \frac{2}{7}\phi_1^Q+\frac{3}{7}\phi_2^Q+\frac{6}{7}\phi_3^Q $$ The Eigenstate Equation is: $$\hat{Q}\phi_n=q_n\phi_n$$ The eigenvalues are the set of possible...
  4. K

    I Is this system a superposition?

    Suppose a blind man builds a machine that paints three apples with three colors, either red, blue or green. Once the machine has done this, are the three apples in the following superposition: or is the wavefunction just one of It feels like because the man is blind, the apples should be in...
  5. H

    I A statement in a superposition of being true and false?

    If a cat can be in a superposition of being dead and alive, why can't a statement be in a superposition of being true and false?
  6. AidenPearce

    B When are particles in a superposition of states?

    Hi guys, I hope you all are doing great. If we take the double slit experiment for instance, before measurement particles are in a superposition of states. Once they are "measured", or non arbitrarily interfered with, their wave function collapses and only one state remains. So my question is...
  7. N

    I Confusion with superposition of states

    Since my major is not physics. My QM knowledge is not pretty good (Mostly self study). I am sorry if this question was asked multiple times in the forum. I've learned that wavefunction can be written as a linear combination of eigenfunctions due to completeness property. If an electron is...
  8. P

    Constant of proportionality in probability of superposition of states

    Using the fact that Pa ∝ |α|^2 and Pb ∝ |β|^2, we get: Pa = k|α|^2 and Pb = k|β|^2 Since the probability of measuring the two states must add up to 1, we have Pa + Pb = 1 => k = 1/(|α|^2 + |β|^2). Substituting this in Pa and Pb, we get: Pa = |α|^2/(|α|^2 + |β|^2) and Pb = |β|^2/(|α|^2 + |β|^2)...
  9. E

    I Energy measurement on superposition of states

    We have a 1 dimensional infinite well (from x=0 to x=L) and the time dependent solution to the wavefunction is the product of the energy eigenstate multiplied by the complex exponential: \Psi_n(x, t) = \sqrt{\frac{2}{L}} \sin(\frac{n\pi x}{L}) e^{-\frac{iE_n}{\hbar}} Now, I want to create a...
  10. E

    I Quantum Computing and Superposition of states

    I'm watching a lecture on the intro to quantum computing. See the attached image which will be useful as I describe my question. So the professor says that we have this single photon and it's in this state, ## | 0 > ##. He states that when we send this photon through a beam splitter that it...
  11. K

    B A couple of questions about photons and superposition..

    There are two polarization filters, A and B. Polarization filter A has angle of 0° and B has an angle of 30°. A photon is in superposition, so it doesn't have a definite polarization axis. The likelihood it's passing through a filter is depend on the difference between angle of the...
  12. R

    Oscillation of a bound particle in a superposition of states

    Homework Statement A bound particle is in a superposition state: \psi(x)=a[\varphi_1(x)e^{-i\omega_1t}+\varphi_2(x)e^{-i\omega_2t}] Calculate <x> and show that the position oscillates. Homework Equations <x>=\int_{-\infty}^{\infty} \psi(x) x \psi^*(x) \mathrm{d}x The Attempt at a...
  13. A

    I Principle of superposition of states

    Upon reading Landau QM, the Principle of superposition of states, I got confused. It states (and i quote): "Suppose that, in a state with wave function Ψ1(q), some measurement leads with certainty to a definite result 1, while in a state with Ψ2(q) it leads to a different result 2. Then it is...
  14. Fetchimus

    Infinite Square Well homework problem

    Homework Statement A particle of mass m, is in an infinite square well of width L, V(x)=0 for 0<x<L, and V(x)=∞, elsewhere. At time t=0,Ψ(x,0) = C[((1+i)/2)*√(2/L)*sin(πx/L) + (1/√L)*sin(2πx/L) in, 0<x<L a) Find C b) Find Ψ(x,t) c) Find <E> as a function of t. d) Find the probability as a...
  15. M

    Understanding superposition of states

    I am wondering if my understanding of superposition concept is correct. Forgive me for not using QM braket notation, I am new on this site and don't know how to embed it in the post. What confuses me about superposition concept is that people often say that some system can be in two (or more)...
  16. B

    Superposition of states, spin 1/2

    Homework Statement Two particles, their spin are 1/2. The hamiltonian is ##H=\gamma s_1 \cdot s_2## At t=0, the state ##|\alpha(0)>## is such as ##s_{1z}|\alpha(0)>=\hbar/2 |\alpha(0)>## and ##s_{2z}|\alpha(0)>=\hbar/2 |\alpha(0)>##. Find the state ##|\alpha(0)>##.2. The attempt at a...
  17. B

    Finding coefficients of superposition of states

    I have some troubles in finding coefficients of superposition of states. I have 2 particles, their spins are s1=3/2 and s2=1/2. At t=0, the system is described by |a(0)>=|3/2, 1/2, 1/2, 1/2> I have to find |a(t)>. I have thought to proceed in the following way: 1) use the basis |s, s_z>...
  18. vtahmoorian

    What makes a superposition of states a coherent superposition?

    Hi everyone I am investigating spontaneously generated coherence(SGC), I found that it happens when an excited atomic state decays to one or more closed atomic levels so that atom goes to a coherent superposition of states , Effect of State Superpositions Created by Spontaneous Emission on...
  19. entropy1

    Macro objects and superposition of states

    Is a living macro object, such as a cat or human being, in fact in a superposition of states? (I am thinking about for instance the multiple-universe idea)
  20. G

    Energy Measurements of Particle in Superposition of States

    Given that E(n) = (n^2)E, and that our wave function PSI = 1/Sqrt(14)(Psi(1) + 2*Psi(2) + 3*Psi(3), what is the the value for the measurement of the energy? So, <H> = SUM((c(n)^2)*E(n)) where E(n) = (n^2)*E and c(1)=1/sqrt(14), c(2)=2/sqrt(14), c(3)=3/sqrt(14), which satisfies...
  21. T

    Superposition of states and orthonormalization

    Homework Statement Consider a particle in a superposition of states given at time t=0 by Y(x,0)=C(y1(x)+y2(x)), where y1(x) and y2(x) are the stationary states with energies E1 and E2 respectively. if y1(x) and y2(x) are orthonormalized, what value of C is required to normalize Y(x,0)...
  22. E

    Electron Transitions: Superposition of States

    It'd be great if you could help me clarify a few things in my head. Firstly I've got written in my notes "quantum mechanics forbids spontaneous transitions from one energy level to another because energy eigenfunctions are time independent". However this seems a bit of a circular...
  23. L

    Probability of superposition of states

    hi could someone please verify that my calculated probability for superposition of states is correct (i derived it myself from a simpler equation) where \Psi=c1\psi1 e^{-iE1t}+c2\psi2 e^{-iE2t} and \psi_i, c_i \in \mathbb{R}...
  24. L

    Superposition of states of the hydrogen atom

    say we had two states \psi1 and \psi2 and i want to model the superposition of the two states \psi=c1\psi1+c2\psi2. how do i find c1 and c2? I've been trying to do c1=\int\psi \psi1 r^2dr over the limits 0 and infinity but i don't seem to be getting anywhere. does anyone have any ideashow i...
  25. D

    Exploring the Effects of Superposition in Harmonic Oscillators

    I think this is a basic question: If a state is in a superposition of energy eigen states of the harmonic oscillator, what will a single measurement yield? Will it be <H>?
  26. G

    Knowledge of the superposition of states

    Is it completely impossible, even in principle, that eventually there can be a device by which we could know about the superposition of states without collapsing it? For example, being able to know that an atom is in a 30% probability of being unexcited and a 70% probability of being excited...
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