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 doubleslit 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.
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_2E_1##, while transitioning to the second state ##E_2\rangle##. In atom's spectrum we can see an absorption line at the corresponding...
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...
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...
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...
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...
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...
Using the fact that
Pa ∝ α^2 and Pb ∝ β^2, we get:
Pa = kα^2 and Pb = kβ^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)...
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...
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...
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...
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...
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...
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...
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)...
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...
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>...
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...
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 multipleuniverse idea)
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...
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)...
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...
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}...
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...
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>?
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...