What is Wave function: Definition and 873 Discussions
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively).
The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state.
For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier transform. Some particles, like electrons and photons, have nonzero spin, and the wave function for such particles includes spin as an intrinsic, discrete degree of freedom; other discrete variables can also be included, such as isospin. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g., a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g., z-component of spin) – these values are often displayed in a column matrix (e.g., a 2 × 1 column vector for a non-relativistic electron with spin 1⁄2).
According to the superposition principle of quantum mechanics, wave functions can be added together and multiplied by complex numbers to form new wave functions and form a Hilbert space. The inner product between two wave functions is a measure of the overlap between the corresponding physical states, and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name "wave function", and gives rise to wave–particle duality. However, the wave function in quantum mechanics describes a kind of physical phenomenon, still open to different interpretations, which fundamentally differs from that of classic mechanical waves.In Born's statistical interpretation in non-relativistic quantum mechanics,
the squared modulus of the wave function, |ψ|2, is a real number interpreted as the probability density of measuring a particle as being at a given place – or having a given momentum – at a given time, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system's degrees of freedom, must be 1 in accordance with the probability interpretation. This general requirement that a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured—its value does not, in isolation, tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.
wave function always refer to the position of particle with probability amplitude. since wave function is not a wave but field, frequency seems meaningless to it. can i imagine it is a vibration field with certain frequency f in complex plane or something?
In flat spacetime, there isn't any problem with wave function collapse. I think that's the "textbook" position, although the only citation I have off the top of my head is the discussion in http://arxiv.org/abs/0706.1232 (section 1.1).
How about in curved spacetime (working in the regime where...
A particle in the infi nite square well potential is found at the 3-rd excited state. What is the
wavelength of the wave function of the particle?
this is a mcq from my faculty who denoted the correct answer to be 2/3 a ...how to get that ?
I am trying to develop a graphical, interactive simulation of a wave function in position space, given an arbitrary potential. It works great, but as a final touch, I would like the user to be able to collapse the wave function, either by measuring its position or its momentum.
My problem is...
Hi
I am currently looking for the wavefunction of the bonding orbital of the hydrogen molecule. Does anybody here know how this one might look like? So, since there is no complete analytical solution for the Hydrogen atom Schrödinger equation, I am currently looking for approximations of this...
hi, i read in quantum mechanics wave function is a combination of eigenfunctions and according to Orthodox interpretation measurement causes the wave function to collapse into one of the eigenfunction of the quantity being measured. Is this explanation still valid?
hi, please explain can by using suitable operator we can find any physical quantity- as by using hamiltonian on wave function we can find energies by the eigenvalues?
thanks
wasi-uz-zaman
I'll write down what i know and point it out if I'm wrong.So we normalize the wave function because -∫|ψ(x,t)|^2dx should always be equal to 1 right? Has this anything to do with transition from ψ to ψ^2?
Apologies if these questions have been answered before - I didn't have any luck with google. Something has bugged me for a while about quantum experiments like Schrödinger's cat where a 'black box' system is theorized to be in a superposition of states until observation causes wave function...
Homework Statement
So I have this normalized wave function
psi=sqrt(2/a) * sin^2(pi*x/a)
with limits of 0 and a.
I'm supposed to find the probability for a bunch of points if this form:
p(x=0.00a,x=0.002a)
Homework Equations
P(a,b)=int(psi^2)dx
The Attempt at a Solution...
We know that electrons are nearly massless so their wave funtion is quite easily detectable.So is there any mathematical relation between the mass of the body and the intensity of the wave it exhibits?
thanks
Homework Statement
The following picture is supposedly periodic (or at least my teacher says so). Could anybody suggest where I begin in order to determine the wave function for this messy graph. Please see the attached for the graph.
Homework Statement
Hello, I have this problem with seemingly simple process, but there are things I either don't know, or make some stupid mistake on the way over and over. Here's the problem:
At a particular time given by the wave function ψ(x)=N*x*exp(-(x/a)2)
Determine N so that the wave...
Hello everybody,
I am currently struggling with a problem that I came across while spending some free time on non-relativistic quantum mechanic problems.
Suppose we have an electron that is describe at time t_0 = 0 by a wave function in position space \psi(x,y,z). Furthermore, assume...
In the cellular method of calculating the band structure:
Why we have to take zero the normal derivative of the wave function at the Wigner-Seitz cell's border?
Homework Statement
Prove the following theorum:
The time-independent wave function ## \psi (x) ## can always be taken to be real (unlike ##\Psi (x,t) ##, which is necessarily complex). This doesn't mean that every solution to the time independent Schrodinger equation is real; what it says is...
Homework Statement
A particle of mass m is in the state ψ(x,t) = Ae-a[mx2/h-bar)+it]
Find A
Homework Equations
I know that to normalize a wave function I should use ∫ψ2 = 1
The Attempt at a Solution
The book gives the solution as 1 = 2abs(A)2∫ e-2amx2/h-bar) dx
My question is...
Homework Statement
A particle of mass m is inside a 1 dimensional "box" of length L such that it's restricted to move between ##x=-L/2## and ##x=L/2## where the potential vanishes.
1)Determine the eigenvalues ##E_n## and the eigenfunctions ##\psi _n## of the Hamiltonian imposing that the...
Hello guys, problem is as follows:
X9) A free electron has energy (kinetic) 10 eV and moves along the positive x-axis.
a) Determine the electron's wave function.
b) The electron reaches a potential step,-V0. Determine V0(expressed in eV), so that the probability of reflectance is 25%.
c)...
Homework Statement
Two-electron Wavefunction: ψ(r1,r2,r12) = exp(-Ar1-Br2-Cr12), r12 = |r1-r2|
A, B, and C are coefficients
Calculate <ψ|δ(r12)|ψ> and <ψ|δ(r1)|ψ>
Homework Equations
NO
The Attempt at a Solution
<ψ|δ(r12)|ψ>
= ∫∫dv1dv2ψ2(r1,r2,r12)δ(r12)...
Wave function is a complex number , why do we have to consider it as a complex number?
Quote:– but there is nothing in the wave equation that restricts them
to being real numbers. If we temporarily suspend disbelief that physical
quantities may be associated with complex amplitudes, then we...
Elementary question:
When one talks of a wave function of a measured object collapsing or decohering or splitting (pick your interpretation), what we base everything on is the measuring pointer. So, which of the following is the case?
(a) one calculates with help of coupling constants etc...
Homework Statement
Normalize the wave function
ψ(x,0) = C1/4 * ea(x2)-ikx a and k are positive real constantsHomework Equations
∫|ψ|2dx = 1The Attempt at a Solution
Now, my maths is a little weak, so I'm struggling a little bit here.
The constant is easy to deal with in all aspects of...
Homework Statement
At time t = 0 a particle is described by the 1D wave function
ψ(x,0) = (2α)^1/4 e^-ikx-α
Verify that this is normalizedHomework Equations
Er! I have just started this sort of thing, so just a bit confused.
I think I can do this if there are limits as to where the particle is...
Homework Statement
Suppose a Gaussian wave packet ψ(x,0) is built out of plane waves according to the amplitude distribution function
A_{k} = \frac{Ca}{\sqrt{\pi}}e^{(-a^2(k-k_{0} )^2)}
Calculate ψ(x,t) for this packet and describe its evolution.
Homework Equations
ψ(x,t) =...
Homework Statement
For the n = 1 harmonic oscillator wave function, find the probability p that, in an experiment which measures position, the particle will be found within a distance d = (mk)-1/4√ħ/2 of the origin. (Hint: Assume that the value of the integral α = ∫01/2 x2e-x2/2 dx is known...
Problem:
Which of the wave functions shown might conceivably have physical significance?
Solution:
I have attached a drawing of the two wave functions. According to my book, the one on the right could have physical significance, while the one on the left does not. Can anyone explain why not...
Just starting QM & am looking at TISE & how it builds from start & need a little help understanding.
OK, for a free particle the de Broglie wave function is
ψdB(x,t) = Aei(kx-ωt)
where A is a complex constant
this corresponds t a free particle with momentum magnitude
p = h/λ = hbar k...
Homework Statement
You have the simple harmonic equation for a transverse wave which is y(x,t)=Acos(10∏t+5x), what is the wave function at the originThe Attempt at a Solution
By "at the origin" does it mean where x=0 and t=0. Because it that case y=Acos0 and therefore y=A. Is that right?
I have been searching for an anwser everywhere, but i can't seem to understand something. In this topic (you don't need to read it) i managed to find out that "we can calculate normalisation factor ##\Psi_0## of a wavefunction ##\Psi## if we integrate probability ##|\Psi|^2## over some volume...
I don't want to argue about whether the notion of "wave function collapse" is a good way of understanding quantum mechanics, or not. For the purposes of this discussion, let's just adopt uncritically the naive approach to quantum mechanics, that:
Between measurements, the system evolves...
Hi
First I should point out that I don't have any scientific knowledge in Quantum Mechanics. I am just enthusiast physicist not professional. I am interested in physics and the only thing that I know for now is Classical Mechanics (Newtonian, Lagrangian and Hamiltonian reformulations) and some...
I'm doing about wavefunctions for my course, I'm a bit confused as to why the wavefunction of Helium has 9 coordinates and time and not 6 coordinates and time. As far as I was aware the wave function was used to describe the movement of electrons around the nucleus of an atom, and it was assumed...
A friend of mine recently tried to tell me that the square of the wave function for a particle (that is, \Psi^2) gives the probability density of finding a particle in space.
I disagree. I always thought that the wave function multiplied by its complex conjugate (that is, \Psi \Psi^*)...
Hi, I've done a lot of personal research on the internet trying to understand what exactly is happening in this experiment but I keep seeing contrasting information about what the role of observation actually had on the experiment.
What I understand is that when they try to figure out which...
I can not seem to find out what a wave function function is amd I would just like a simple explination of what it is and how it is used. And what is this symbol ψ. Thank you.
I hear some reasons that photon exist in 4D space-time, wave function not and so on.
But, an electron can be described with de Broglie waving and we can use wave function to describe electron. Frequency of the wave function is the same as energy/\hbar and k of wave function is the same as...
I was trying to understand wave function collapse in terms of superposition, but I ran into some problems when relating back to information theory/entropy. It is given in the definition of information in terms of entropy energy is needed to transfer information. That is something we have always...
Homework Statement
A particle is in the state
1/2 |1> - 1/2 |2> + 1/2 |3> - 1/2 |4>
A detector is placed to measure state |4>. What the particle's wave function collapses into, if the detector does not find a particle
Homework Equations
<i|j> = delta (i, j)
The Attempt at a...
Homework Statement
A particle in the infinite square well has its initial wave function an even mixture of the first two stationary states:
\Psi(x,0) = A\left[ \psi_1(x) + \psi_2(x) \right]
Normalize \Psi(x,0). Exploit the orthonormality of \psi_1 and \psi_2
Homework Equations
\psi_n(x) =...
As I understand it the wave function itself does not carry any physical interpration. Rather it is the square of it's absolute value. But that forces the question: Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as...
When dealing with n-particle systems that are identical, is the superposition of them just a mathematical construct, or is it similar to how the state of a single particle can be in multiple eigenstates until its measured.
For instance, if I have two fermions: \Psi = \Psi_a(x_1)\Psi_b(x_2) -...
Find the probability current of Ae^i(kx - ωt) + Be^-i(kx+ωt)
Ok, to my understanding the probability current is the probability that you will find a certain particle as it moves with time, thus the probability of finding it changes with time. Quantum physics is a tricky one to grasp, I've...
I understand a normal mechanical wave, simply a disturbance that moves.
But, I want understand a quantum wave function, mainly how you can describe a wave by the particle it self?
So, I am reading this paper on the physicality of the wave function and I have a question.
Here's the passage:
"If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus, there will exist...
Homework Statement
ψ(x)=A((2kx)-(kx)^2)
0≤X≤2/k
ψ(x)=0 everywhere else
I need to find A
Homework Equations
∫|ψ(x)|^2 dx=1
so I know I need to evaluate it between 0 and 2/k
The Attempt at a Solution
My problem is do I square the whole ψ(x)? If some one could point me in right direction I...