Wave function Definition and 865 Threads

1. Homework Statement p: momentum x: position t: time h_bar: Planck's constant Ψ: wave function Homework Equations The Attempt at a Solution I've posted a link to pictures. http://imgur.com/a/TKvUu I'm not vera good at using LaTex yet :( So I've shown that the wave equation satisfied the...

For theoretical sake, would a collapsed wave function combined with a non-collapsed wave function result in a wave function between that of a collapsed and non- collapsed wave function? Thank you and please excuse the stupidity of the question

Could someone please explain Schrödinger's equation and what each letter in it represents and how to apply it? Thank you

I've been given the question "What is ∇exp(ip⋅r/ħ) ?" I recognise that this is the del operator acting on a wave function but using the dot product of momentum and position in the wave function is new to me. The dot product is always scalar so I was wondering if it would be correct in writing...

Homework Statement A particle has a given wavefunction: ##ψ(x) = C e^{-x}(1-e^{-x})## (many steps in between) ... Find the most probable position of the particle Homework Equations Most probable is where the probability density's derivative = 0. Right? ##P(x) = |ψ(x)|^{2}## The Attempt at a...

Homework Statement Consider a free particle, initially with a well defined momentum ##p_0##, whose wave function is well approximated by a plane wave. At ##t=0##, the particle is localized in a region ##-\frac{a}{2}\leq x \leq\frac{a}{2}##, so that its wave function is...

Excuse my ignorance. I've been googling trying to understand but they always seem to just state it without explaining why. They say the electron could be anywhere within this area of probability but we don't know why until we look and then the wave function 'collapses' and we know where it is...

How are these pictures taken of the electron wave function without the wave function collapsing? Does this mean that electron wave functions are real waves after all? Wikipedia Quantum cascade laser will give you the discription

What is a Prolate Spheroid Wave Function and how does it apply to EEGs and brain mapping ?Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit http://www.sciencedirect.com/science/article/pii/S1063520306000650...

I have been trying to understand the wave function around an atom.. Is it more like a soccer ball where the shell is smooth but is more likely to be found in say the dark areas, or is it more like a golf ball where it is not only angularly undulating, but also radially undulating?

I've got a question for you all. if there is a wave-function for a single particle, such as a photon.. and there is a wave-function for an electron.. "A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function...

From what I understand in laymans terms (Since I am a beginner). In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome. The...

I am wondering if there are some views on this. One of the key mysteries of the double slit experiment boils down to when the observation mechanism is placed by one of the slits - and switched on it triggers the change from wave-like outcomes to particle-like outcomes. Is it the observation or...

For example, let's say that psi(q) is the wave function of an electron(which describes/represents the electron) that is located in an atom and isolated/unentangled from the rest of the system. What is the wave function value of this psi(q) ? What is the wave function for that whole atom(with...

For example let's say that psi(q) is the wave function of an electron(which describes/represent the electron) that is located in an atom and isolated/unentangled from the rest of the system. What is the wave function value of this psi(q) ?What is the wave function for that whole atom(with only...

Hello Guys, I am trying to Normalize the following wave function but I am getting stuck in between (Maybe maths is the problem here for me). Can anyone please provide some hints. The Wave Function is ψ = e - |x| sin (α x)Please help.

Suppose the system is in a state of superposition of two determinate states (of an observable) and has equal probability of getting each determinate state, when observed. An observation forces the collapse of the wave function to either one of the determinate state (say, states A and B). Since...

Assuming the 2s and 2p wavefunctions are normalized, determine the coefficients in the hybrid orbital: Ψ(sp3) = aΨ(2s) + aΨ(2px) + aΨ(2py) + aΨ(2pz) (the other 3 hybrids have – signs for some of the coefficients. [SIZE=16px]I have no clue where to start. I know this is a tetrahedral hybrid...

What is wave function?? For example Prepare identically same system and observe position. Then collect result of all position value. Is it position wave function??

Homework Statement Serway's Physics for Sciencetists and Engineers with Modern Physics, 9th Edition (current), Chapter 16, problem 19:[/B] (a) Write the expression for y as a function of x and t in SI units for a sinusoidal wave traveling along a rope in the negative x direction with the...

Hi I thought I knew the answer to this question until I encountered the following question: What is the unit of R(r)? We are of course talking about the radial part of the solution to Schrodinger's equation in spherical coordinates (i.e. \psi(r,\theta,\phi) = R(r)\Theta(\theta)\Phi(\phi)). I...

Hi dear people , Hello I waw studying super position of two Sound Waves , traveling in same medium with same frequency , same wavelength and same amplitude while differing in phase . quick derivation : Wave 1 displacement y1= A sin (kx-vt ) and wave 2 displacement y2= A sin (kx-vt-phase...

Homework Statement so there is this problem : find the amplitude from the superposition of Z1 and Z2 where Z1 : 8 sin 100t, A1= 8m and Z2 : 6 sin (100t-pi/2), A2=6m Homework Equations i know that all we need to do is add them and do the trig using sine additon, but i couldn't do that because...

I was just wondering, when particles interact with a force (which would be all the time) , does it cause the wave function to collapse? If so does that mean particles interact with forces in small time periods, since we know particles exist as a probability function? I just assumed that fields...

Homework Statement Homework Equations The Attempt at a Solution a) I am not sure exactly what they are looking for, but I said that the operators associate, distribute, and do not necessarily commute. b) I know by definition ##\langle a' \mid a \rangle = \int a'^{*}a dx = \delta_{a'a}##...

Suppose there is a wave function for a particle. What is the actual meaning of hermition conjugate of the wave function? Does the conjugate represent any other state of the wave function? What is the physical meaning of product of wave function and its conjugate? Please explain. Thanks in advance.

I am following the math of scattering theory in Sakurai, Revised Edition pp.380-381 For a free particle, one can find that the solution is a plane wave that can be written (in position space) as, <x|\phi>=\frac{e^{ip \cdot x}}{(2 \pi \hbar)^{3/2}} However, how does one obtain ##<x|p>?## In...

Gauge transformation can be written as: ##\psi(\vec{r},t)\rightarrow e^{-i \frac{e}{\hbar c}f(\vec{r},t)}\psi(\vec{r},t)## http://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html Does it have any sense that we choose such function ##f##, that all right side is constant in time. Is this...

I read that a wave function of the photon does not exist in coordinate space. But, when I read Feynman's "QED: the strange theory of light and Matter", for instance, when the photons travel through the glass, it seems like wave functions of photons. How it is with this?

Hi, is the wave function that couples to the Dirac equation the same as that which couples to the Schrodinger equation? Thanks.

I'm trying to understand the delayed choice quantum eraser experiment without consciousness. As I understand it, photons will either interfere or not depending on whether or not "which-path" information is randomly hidden and rendered unkowable to the experimenter. That is, rather the by any...

I've recently been reading the book The Dancing Wu Li Masters which is supposed to be a very basic introduction to quantum physics. I have a question on the following quote: "Up to now, we have said that the collapse occurs when somebody looks at the observed system. This is only one point of...

Homework Statement Let ##|\psi\rangle \to |\psi'\rangle = \hat{T}(\delta x)|\psi\rangle## for infinitesimal ##\delta x##. Show that ##\langle x \rangle = \langle x \rangle + \delta x## and ##\langle p_x \rangle = \langle p_x\rangle.## Homework Equations ##\hat{T}(\delta x) =...

Homework Statement The wave function of a certain particle is Ψ= A cos^2(x) for -π/2 < x < π/2. Find the value of A. Homework EquationsThe Attempt at a Solution My answer is coming out to be zero wheres as the correct answer is under root 8/3π ... Please help me out !

Hello! (Wave) A function of the form $$u(x,t)=A \cos{(kx-\omega t)}, \text{ where } k>0, \omega>0, A>0$$ is called wave function. If in addition $u(x,t)$ is the solution of a differential equation with partial derivatives we are talking about a solution of the differential equation in the...

While I was daydreaming in my boring math class today I came across a weird problem. What ACTUALLY causes a wave function to collapse. I had a discussion with my teacher the week prior and she was telling me that it has something to do with your brain. I didnt really believe her, I just thought...

Hi. I would like to know which variables in the wave function are constant (in this local context) and which are not. The wave number for instance varies in the article I was reading (WKB approximation). Why is this so? What other variable in the wavefunction can vary? Please help me as I am...

Is the wave function of quantum mechanics considered to be the quint-essential invariant object? Is it the wave function that must not change with space, time, gravitational field, etc? It would seem to me that the relative probabilities that things happen is the thing that can not change with...

Hi, I was studying the solution of Schrodinger equation with no potential and found that the wave function is just a single plane wave eikx for movement of the particle in positive x direction. But when the phase velocity of a single wave is calculated it turns out to be less than the...

I have read the following from what seems a reliable source: The identification of the spacetime interval with quantum phase applies to null intervals as well, consistent with the fact that the quantum phase of a photon does not advance at all between its emission and absorption. Hence the...

... and its classical wave equation? Suppose in our double sit experimental setup with the usual notion of d,D we have a light of known frequency (v) and wavelength (L)- so its y=Asin(kx-wt). It passes through the two hole and move ahead doing the usual interference stuff, so final wave equation...

Suppose I have a region from 0 to L. I have a barrier potential V from x1 to x2, such that 0<x1<x2<L. The potential is 0 everywhere. I have obtained the wave-function by considering the propagation from left to right. Now if I consider the propagation from right to left should I get a different...

Edit: I forgot to add the picture, and I'm having trouble adding it from Tapatalk. I'll add it soon. I'm trying to understand the derivation in my textbook of the wave function for a potential step. The derivation reaches the step shown in the attached photo, which I am fine with. However, the...

Homework Statement A woman is walking along a road. She has a mass of 52 kg and is walking at 1 m/s. (a) She is not paying careful attention and is walking straight towards the wall of a nearby building. Assume that the wall is infinitely hard and that she can be described as a plane wave (a...

I have a number of questions about the wave function - 1. Do photons have wave functions like the one in Schrodinger equation? 2. If they do, when you send out a wave function with a certain wavelength, then because you know the momentum with no uncertainty the uncertainty of the position...

Is there a way to mathematically describe the space where wave functions overlap like with how wave functions describe the space a particle could exist. Then if that is possible can you determine the time period at which that overlap will occur.

λ∂Homework Statement Aguitar string lies along the x-axis when in equilibrium. The end of the string at x=0 (the bridge of the guitar) is fixed. A sinusoidal wave with amplitude A=0.750 mm and frequency f =440 Hz, corresponding to the red curves in Fig. 15.24, travels along the string in the...

If you are given the state of a system at t=0 in vector form, how do you find the wave function for arbitrary t?

Is the collapse of the wave function of the electron in the double slit experiment based purely on the act of observation? Or could it be that the way the instrument used to measure the electron caused it to collapse by how it physically interacted with the electron? Keep in mind the delayed...

I am trying to find the most probably distance of the electron from the nucleus of a ground state hydrogen atom. The wave function is given as the following: $$\psi_{1,0,0}(r,\theta,\Phi)=R_{1,0}(r) \cdot Y_{1,0}(\theta, \Phi)$$ I remember that the probability function is $\psi^2$, but why do...