# Superposition of states Definition and 7 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. ### 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...
2. ### 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...
3. ### 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...
4. ### 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?
5. ### 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...
6. ### 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...
7. ### 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...