Wave function Definition and 865 Threads

Hi there, I took the course of quantum mechanics long time ago. From there I learn how to describe an atom with wave function. For example, Hydrogen has the wave function in (spherical coordinates) space. In the book they consider a reduced mass for the nucleus and the only external electron...

Let's say that there's a box of height, h, length, l, and width, w, and within the box there's a proton. Thus it's certain that the proton would be inside the box. A slide is then put halfway along the length of the box. Thus the proability that the proton is in one side of the box is 0.5...

I've been studying the basics of the quantum mechanics, and I found the continuity restraints of the wave function quite suspicious. What if there is a jump discontinuity on a wave function where the first derivative of which is still continuous? What is the problem with such wave function?

Why does STRONG FORCE fail regarding complex structures of sub atomic particles when wave functions collapse @ entangled superpositions. Why does it not continue to function keeping the particles bound yet unentangled with the observed Eigenstate being it was originally binding such particles @...

My level is not sufficient enough to easily understand QFT yet there is some basic question I need to understand in it - what in QFT corresponds to a wave function in QM, for a single particle case and, say, for a more general case of multiparticle nonseparable state (suppose the particles are...

Hi, under what equation does the Dirac Equation fall under versus that of the Wave Function. Why is Antimatter from Dirac Equation really there but the wave function is not real? Because if Antimatter exist from an equation of complex numbers.. why can't the wave function be real too?

What instrument can affect wave function of object? If wave function doesn't have any locality. Then why can't an instrument here able to access and alter the wave function of any object in the world (and detectable in the other side of the planet)? How do you make such experiments. And what...

Assume that i have a wave function of holes in a solid, can we derive the wave function of electrons? If can then how?

Hi, I just completed my second year of my physics undergraduate degree. And recently did a course on Quantum Mechanics. I have a few questions regarding the basic theory and postulates, probably, because due to lack of full clarity. So, Consider a wave function ψ(x,o), which is well behaved and...

Homework Statement Assume a particle with a wave function ##\psi(x)## such that ##-\infty < x < \infty##, that move under some potential ##V(x)##. Show that: a) two wave functions with same energies can only differ by a complex phase; b) if the potential is real, then you can choose the wave...

The problem is actually of an introductory leven in Quantum Mechanics. I am doing a course on atomic and molecular physics and they wanted us to practice again some of the basics. I want to know where I went conceptually wrong because my answer doesn't give a total probability of one, which of...

In cylindrical coordinates could Ψ=f(r)exp[-i(Et-pz+Φ/2)] be a valid quantum mechanical wave-function for the right boundary conditions and with the right choice of f(r)? Thanks!

Hello. It is said that if we exchange two electrons, we can't tell which is which. Identical mass, charge, etc. So if I hold two electrons, one in each hand, and someone switched them, I wouldn't be able to know. But one way to distinguish particles is their trajectory. If I have a very long 1D...

Meant as element of Hilbert space of L^2 functions... etc., the wave function is a vector. In the abstract description with kets and operators on these, the wave function is the scalar product between a ket |Psi> and the "eigenkets" |x> of the position operator: psi(x) = <x|Psi>. So: psi is a...

Why is the triplet state space wave function ΨT1=[1σ*(r1)1σ(r2)-1σ(r1)1σ*(r2)] (ie. subtractive)? How does it relate to its antisymmetric nature? Also, why is this opposite for the spin wave function α(1)β(2)+β(1)α(2) (ie. additive)? And why is this one symmetric even though it describes the...

In the Wilsonian viewpoint, quantum electrodynamics is an effective theory, where the low energy predictions are obtained by coarse graining eg. some form of lattice QED where the lattice is taken very finely. In the Copenhagen interpretation, we are agnostic as to whether the wave function is...

My question is, how does one get a wave function for a 'combined' spin-1 and a spin-0 field? How is this possible? I have only been able to find combined states for equal spin identical particles. If you don't understand my question, I'll be glad to reword it.

Homework Statement Given the following wave function valid over -a \le x \le a and which is 0 elsewhere, \psi(x) = 1/\sqrt{2a} Find the uncertainty in \left<\left(\Delta p\right)^2\right> momentum, and the uncertainty product \left<\left(\Delta x\right)^2\right>\left<\left(\Delta...

By the Principle of Superposition, a state vector can be defined as pic.01 also, the state vector can represent a wave function in a continuous case as pic.02 My (1) question is, in pic.03, why the state vector can be pulled out from the integral? I have an idea but I think it should be...

Let ##\alpha(n)## and ##\beta(n)## be the eigenfunctions of ##S_z## that correspond to "spin up" and "spin down" for electron ##n## respectively. (a) Suppose we prepare electron ##1## to have its spin aligned along the ##x## axis. Is its spin wave function...

http://vallance.chem.ox.ac.uk/pdfs/VariationPrincipleNotes.pdf In the proof above I need to understand why: $$S_{ij}=S_{ji}$$. Which is the same as proving $$\int f_i f_j dg=\int f_j f_i dg$$ (I) Not sure about what I should call the variable for so I called it g. Can someone prove this...

Can a singe particle have a different wave function for different observers? Suppose someone at rest prepares some electrons with an (close to exact) momentum. In his rest frame the position of the electron is not known. But what kind of wave function will a person see traveling in the same...

Homework Statement I am trying to solve a problem from a popular quantum mechanics text. I am learning on my own. I am trying to calculate the variance, which is <x^2>-<x>^2 = variance in x. I posted a photo of the problem as a picture that is linked below as well as the solution, I simply...

In interpretations without natural factorizations, the cat won't just be dead or alive. It won't even be a cat. So let's say the cat is isolated in a box totally shielded from any decoherence from any environment.. and the any factorization between system and environment inside the box is...

Hi guys, Greetings! I have a confusion about the wave function of a traveling wave. This is the wave function of a traveling wave traveling towards the positive direction of x axis u(x,t)=Acos[ω(t-x/v)+φ0], where v is the velocity of the wave, ω is the angular...

For hydrogen atom ground state we know φ=π-1/2a-3/2e-r/1 I want to know the complex conjugate of φ* ?

The following equation (5.122) is the minimum-uncertainty wave function, which is a Gaussian wave packet. Since it is Gaussian in ##x##, we may get ##\Delta x## directly from the ##\sigma## of the Gaussian distribution: ##(\Delta x)^2=\frac{\hbar^2}{2(\Delta p_x)^2}##. We have ##\Delta x\Delta...

Homework Statement The wave function for lithium can be written as: | 1sα(1) 1sβ(1) 2sα(1) | ##\frac{1}{\sqrt(3)} ## = ψ(1,2,3) | 1sα(2) 1sβ(2) 2sα(2) | | 1sα(1) 1sβ(2) 2sα(1) | How can each row be a linear combination of atomic orbitals that makes a new orbital in which the electron...

"To visualize the standing waves (or orbitals) of electrons bound to a positively charged nucleus in three dimensions, we will need a four-dimensional plot of the wave function vs. x, y, and z." http://www.grandinetti.org/electron-orbital-shapes"The wavefunctions in the N=2 family are vectors in...

Suppose I measure the position of a particle, and I find it to be at point C. By deterministic, I mean if we know the wave function of the measuring instrument (and of course also the wave function of the particle before measurement) then we can, in principle, know that the particle is going to...

If wave is a real concept, then why we have a complex(imaginary) part associated with the wave function?

Does the indeterminacy of quantum mechanics arise from the lack of knowledge of the time-evolution of the wave function between measurements or do it have another origin

Hey there - I think I have an issue with my 3D density plots of the probability density of the Coulomb wave function. The reason I think something is going wrong is because my plots of |ψ(n=2, l=1, m=-1)|² and |ψ(2, 1, 1)|² are identical, while I would expect them to have the same shape but be...

Hey there, I used Mathematica to find the (non-normalised) wave function of an electron in the vicinity of a Hydrogen nucleus, and converted the answer from one involving Whittaker functions to one involving generalised Laguerre polynomials. My result is shown below: This agrees with the...

Sorry if this is a silly question, I was just womdering about it. So instead of putting Schrodinger's cat in a box we put in a room and instead of realising poison and thus killing it we push it from from one end of the room to the other end. We will be able to notice that the force of...

Depending on interpretation of QM, can hilbert space be considered just as real as space time? In MWI the wave function is real, but still lies in hilbert space, so would hilbert space be considered a real space according to this interpretation?

I have been following Leonard Susskind's 'Theoretical Minimum' lecture series on quantum mechanics he made in winter 2012, and have, at least up to lecture 7/8, understood what he is doing - he has primarily been looking at systems of single spin 1/2 particles and pairs of them, examining...

i don't understand why wave is a function of both time and distance and i think one is enough.can some one explain that to me?

Homework Statement Using the following expression for the Dirac delta function: $$\delta(k-k')=\frac{1}{2\pi} \int_{-\infty}^{\infty}e^{i(k-k')x} \mathrm{d}x$$ Show that if a position space wave function $$\Psi(x,t)$$ is normalized at time t=0, then it is also true that the corresponding...

Homework Statement Consider a particle in an infinite square well potential that has the initial wave-function: Ψ(x,0) = (1/√2) [Ψ_1(x) + Ψ_2(x)] where Ψ_1(x) and Ψ_2(x) are the ground and first excited state wavefunctions. We notice that <x> oscillates in time. FIND the frequency of...

I want to know how this integral will equal zero? I know that Ψ will fall to zero as x goes to infinity and i know that Ψ must fall to zero very quickly , Ψ must fall to zero faster than 1/√|x| all of this will help evaluating this integral i tried to solve it as follows The first term...

In interpretations where the wave function is real, what does that mean? does it mean that the wave function has physical meaning?

Hi. I am struggling to understand the concept of distinguishability in quantum mechanics. If the wave functions of two particles overlap, those become indistinguishable from what I can understand. So if, in an atom, two electrons occupying an orbital are also indistinguishable. right? But can't...

Hello I am not professional at physics and new on this forum so don't be angry when I make mistakes So my question is about wave function so is it right that ψ=Asin(kx)+Bcos(kx) where A and B are constants, k is a some constant k=√2mE/ħ^2 and x is cordinate so when we give A and B value and do...

1. The scenario If we have a small cuboid volume embedded in a larger dito with periodic boundary conditions, and a wave function that is constant inside the former, while zero everywhere else; what can we then know about the momentum? Homework Equations I. Âψ = Aψ (A being the measured...

What information can one obtain from wave function?

Homework Statement A particle is described by the state of the following wave function. wavefunction(x,y) = 30/[(a^5)(b^5)]^1/2 * x(a-x) * b(b-y) Homework Equations integral from 0 to i of x^n * (1-x)^m dx = (n!m!)/(n+m+1)! The Attempt at a Solution I know that normalizing means taking the...

Are my thoughts correct? **Wave function just means the wave function psi. I will specify when the wave function is squared. 1.) Schrodinger's Equation describes particles-their position, energy, spin (through the "numbers" l, n, and m). 2.) Simplified, SE says the total energy is the sum of...

In QM, the wave function is a wave in hilbert space. But is it possible that it is a physical wave in physical space? I think that there are a few interpretations/theories of QM that describe it as a physical wave.

I understand that ψ goes to zero as x goes to infinity. Is it also true that dψ/dx must go to zero as x goes to infinity?