Wave function Definition and 865 Threads

Homework Statement This problem is in Schaum's outline of quantum physics. We need to evaluate |\psi(x)|^2 for the wave function \psi(x)=\int_{-\infty}^{\infty}e^{-|k|/k_0}e^{ikx} dk Homework Equations |\psi(x)|^2=\psi(x)\psi(x)^* The Attempt at a Solution I tried to evaluate the...

Homework Statement Okay, so i have a wave function from a particle in an infinite square well that has an initiate wave function with an even mixture of the first two stationary states. ψ(x,0) = A[ψ1(x) + ψ2(x)] a. Normalize ψ(x,0) b Find ψ(x,t) and |ψ(x,t)|2 (use Euler's formula...

Ok so when observed, the wavefunction collapses, can someone delicately explain the maths behind it? Or send me to a page with a coherent explanation, that is followable for a first year undergrad? I've covered Eigenvectors briefly in my algebra course last semester and i find that the...

At t = 0 a particle is in the (normalized) state: \Psi(x, 0) = B \sin(\frac{\pi}{2a}x)\cos(\frac{7\pi}{2a}x) With B = \sqrt{\frac{2}{a}}. Show that this can be rewritten in the form \Psi(x, 0) = c \psi_3(x) + d \psi_4(x) We can rewrite this to: \Psi(x, 0) = \frac{B}{2}\left[ c...

The plane wave function sometimes could be represented as: U(\mathbf{r} ,t ) = A_{0} e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t + \phi)} and we could separate the expression above into: U(\mathbf{r} ,t = \cos(\mathbf{k} \cdot \mathbf{r} - \omega t + \phi) + i \sin(\mathbf{k}...

Homework Statement This is problem 2.22 from D.J. Griffiths Introduction to Quantum Mechanics A free particle has the initial wave function: \Psi(x,0)=Ae^{-ax^{2}} Find \Psi(x,t). Hint Integrals of the form: \int_{-\infty}^{\infty}e^{-(ax^{2}+bx)}dx can be handled by completing the square...

Homework Statement Below is a wave function that is a linear combination of 2 stationary states of the infinite square well potential. Where ψ1(x) and ψ2(x) are the normalized solution of the time independent Schrodinger equation for n=1 and n=2 states. Show that the wave function is...

I have a question regarding Young's double slits experiment. To my understanding, wave function of a photon somehow collapses according to the probability function (which has a interference pattern). But at the very moment the wave hits the screen, it seems to me that there should be no...

Wave function is always in abstract space in any quantum interpretation be it Copenhagen or Bohmian or Many Worlds because wave function is in many dimensional abstract Hilbert Space. Correct? Since the counterpart of Hilbert space in QM is Fock Space in QFT. Then the fields in QFT live in...

helo can someone tell me where I can find detailed explanation about normalization and orthogonal properties of the radial functions since the books I've been reading do not explain enough, I thought Laguerre associated polynomials resolved the problem directly but this is not the case, the...

Homework Statement A particle of mass 'm' moves in a 1-dimensional harmonic oscillator potential. The particle is in the first excited state. Calculate < x >, < x^2 >, < p >, and < p^2 >. Homework Equations Harmonic oscillating potential ---> V = (1/2) K x^2 First excited state...

Homework Statement Find the momentum-space wave function for the nth stationary state of the infinite square well. Homework Equations Nth state position-space wavefunction: \Psi_n(x,t) = \sqrt(\frac{2}{a})sin(\frac{n\pi}{a}x)e^{-iE_nt/\hbar}. Momentum operator in position space: \hat{p} =...

Homework Statement Hi, i would to resolve this problem of quantum mechanics. I have hamiltonian operator of a unidimensional system: \hat{H}={\hat{p}^2 \over 2 m}-F\hat{x} where m and F are costant; the state is described by the function wave at t=0 \psi (x, t=0)=A e ^{-x^2-x} where A is...

Homework Statement Not a homework problem, just a general question that I find confusing. Homework Equations The Attempt at a Solution So, back in Trigonometry and Classical Mechanics I learned that the equation that best represents a wave. Now, Solving the differential equation that...

Homework Statement we have a particle in an infinite square well from x=0 to x=L/2 Then it says that we suddenly move the right hand side of the wall to x=L and then it asks to find the probability that the particle is in the ground state of the widened well. The Attempt at a Solution...

Hello, Say I have a system with a spatial part and a spin degree of freedom, hence the wavefunction generally looks like \psi_+(\textbf r) |+\rangle + \psi_-(\textbf r) |- \rangle w.r.t. for example the z-axis. Now what if I'm simply interested in the spatial part? Can I perform an...

Homework Statement A particle of mass m is moving in one dimension in a potential V(x,t). The wave function for the particle is: ψ = Axe^([-sqrt(km)/2h_bar]*x^2)e^([-isqrt(k/m)]*3t/2). For -infinitity < x < infinity, where k and A are constants. Normalize this wave function. Homework...

Hello there, could anyone help me with a certain basic problem in relativistic QM? What would be the wave function of a photon (or generally a particle with zero rest mass) in a spherical 3D cavity, having potential energy V=0 within the cavity and V=k outside the sphere (k>0)? I have been...

As I understand it, where a system’s Hamiltonian is not time-dependent, the wave function of a system that is in state psi(0) at time t=0 evolves as: psi(t) = sum, over all eigenvalues E of operator H, of exp(-i*E*t / hbar) * <E|psi(0)> * | E> If the eigenvalues are continuous it is an...

Hello, I was under the impression that a dirac delta was a "legitimate" state for a particle: maybe not mathematically, but least physically. But I was recently told by a post-doc in QM that if your particle is in a dirac delta state at one moment, the very next moment the particle is...

Homework Statement Consider a Wavefunction: \psi(x,y,z)=K(x+y+x^2-y^2)e^{-r/a} Find expectation value of L^{2} , L_{z}^{2}, L_{x}^{2}. Homework Equations The Attempt at a Solution The first step would be a rewriting a wavefunction in terms of spherical coordinates: \psi=Kr(\cos\phi \sin...

I like to know in one dimensional symmetric potentials, can we have any even wave functions which be zero in the origin?

hi , can anyone please explain to me what is wavefunction - and can we apply schordinger wsve equation to simple pendulum. thanks

"Optimizing" a Wave Function Homework Statement Consider a Hydrogen Atom, an electron in an attractive Coulomb potential of the form V(r)=-\frac{e_0^2}{4\pi\epsilon_0r}, where e0 is the elementary charge. Assume the following wave function for the electron (with α>0): \psi(r)=Ae^{-\alpha...

we know that if we send one electron through 2 slit, the wave function on the curtain(detector) is a wave that it's maximum is in the center. and we can find electron anywhere on the curtain according to it's probability. but i want to know whether we observe the electron on all part of the...

Dear friends In quantum mechanics what is the physical significance of normalizing a wave function? Thanks in well advance

Can anybody please explain the reason why a normalizable wave function ψ(x) → 0 faster than 1/√x as x → ∞. I can understand the reason why ∫ψψ*dx < ∞ But do not understand how quadratic integrability implies that. I would be very thankful to anybody who can give me some idea.

Homework Statement Show that radial components of the continuum electron wave function satisfies the radial equation: {\left[\frac{-\hbar }{2m}\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial }{\partial r}\right)+\frac{\hbar ^2l(l+1)}{2m r^2}-\frac{Z e^2}{r}\right]R=E R}...

Ψ(x,t)=A⋅exp(A|x|)⋅exp(−iωt) Consider the one-dimensional, time-dependent wave function for infinite motion: (x,t) = Ae–a|x| e–it where A, a, and  are positive real constants. What are: (a) normalization constant A, (b) the quantum-mechanical expectation value of coordinate x...

consider a atom who's single electron is made to jump into conduction band ,after some time the electron will come into it's valence band by releasing the quanta of energy but if an observer observes the electron in it's excited state continuously it's wave function will collapse to bring about...

Can anyone help me, I am some what unclear on the reason why "conventional" superconductors have cooper pairs only in the singlet state. Is it something to do with the expectation values given for the separate states calculated from their spatial and spin wave functions? For example does the...

The postulates of quantum mechanics include: (1) Schrodinger's equation describes how the wave function of a system changes over time, and appears to make the wave function continuous over time. (2) When a measurement is made of quantity m, the wave function instantly changes to an...

I was walking to lecture and normally there are several doors leading to the lecture hall, but for some reason all of them were locked except for one... when I tried to go through the only unlocked door, my wave function just collapsed! I'm scared and I don't know what to do...

I obtained the following from a book. Question is: Periodic Sawtooth described by the following; f(x) = x/2∏ for 0<x<2∏ f(x+2∏) = f(x) for -∞<x<+∞ The solution is: If x = 0 y = 0 If x = 2∏ y = 2∏/2∏ = 1 If x = 4∏ y = f(2∏+2∏) = 2∏ = 1 Can anyone...

i just started studying quantum mechanics in my college...i asked a number of teachers and seniors that why psi(ψ) is maximum at r=0, also (ψ)^2 is maximum at r=0 but probability is maximum at r= a(knot) for 1s orbital this seems a contradiction to me that on one side we are ssaying ψ is...

I am reading Shankar's "Principles of Quantum Mechanics" and am up to the part where he uses Schrodinger's equation to derive the wave function for various 'simple' scenarios in one spatial dimension. The first few were fine but his presentation of the step potential problem (specifically...

As we all know, we can write schrodinger equation in Linear algebraic form. Also, Dirac had introduced his matrix mechanics. And we can write any linear operator as matrix. and so on... How can we write wave function as matrix? What is the dimension of this matrix?

Dear generous and helpful physicists, A number of threads here contemplate strategies for transmitting information faster than light by observing an entangled particle in one place, allegedly causing the wave function of its entangled twin to instantly collapse in another, far away place...

Does the wave function represent the physical state of the system (MW) or merely our information about the system (orthodox interpretation)? If it represents something in between (Bohmian), what does that imply? Furthermore, if QM is supposed to be more “fundamental” than classical physics, does...

I'm getting bogged down in what is probably a very basic subject and it's holding me back. I'm not really sure how to determine the wave function \psi(x,t) given a function \psi(x,t=0); and since this is pretty much the under-pinning of every homework problem I've seen so far it's a huge issue...

I am teaching myself quantum mechanics and have just read the particle in a box explanation, which is the first derivation of a theoretical reason why only discrete energy levels are possible within certain bound scenarios. In Shankar, the argument uses a requirement that the wave function...

Homework Statement Prove that the spherical harmonic wave function \frac{1}{r}e^{i(kr-{\omega}t)} is a solution of the three-dimensional wave equation, where r = (x^2+y^2+z^2)^{\frac{1}{2}} . The proof is easier if spherical coordinates are used. Homework Equations Wave function...

Hi, I have been looking for explanation,how to draw angular part of wave function and I have found in physicsforums.com/archive answer to my question by user Gokul43201. He posted this: The trick is in being able to draw polar plots roughly, from the spherical harmonics. Consider the...

Homework Statement In a book I found the following calculation without the way. How do you get from 1) to 2)? Homework Equations (1) \Psi(x,t)=\frac{A}{2\pi}\sqrt{\frac{\pi}{d²+i\frac{\hbar t}{2m}}} exp{\frac{-\frac{x²}{4}+id²k_{0}(x-\frac{k_{0}\hbar}{2m}t)}{d²+i\frac{\hbar t}{2m}}}...

I'd like to get some help and pointers on how to derive a wave function. Since I'm not really good at physics I'm just going to use brute force, if anyone spot a mistake please please point it out. If I look at an electron in an well with infinite potential walls. The well has the dimensions...

in a double slit experiment, if we find which-way and then stop observing the photon and send it again through another double slit (kept in, say, series), would an interference pattern occur?...the second time around

Homework Statement Using the results of the previous problem, find [x,p2 ] and from that determine [x,p2 ]\psi(x) Homework Equations The solution to the previous problem was [A,BC]=[A,B]C+B[A,C] The Attempt at a Solution As I'm suppose to use the results of the previous problem I...

Homework Statement Consider the wave described by: E= 3 sin [pi (x/c - t)*10^13+ pi/6] True or false? 34. The frequency = 10E13 Hz. 35. The wavelength = 3E-6 m. 36. The direction of motion: positive x direction. 37. The speed = 300 000 km/s. 38. The maximum amplitude = 9...

Hello again! Say I have a potential well, between 0 and a. I also know how the wave function looks like for (t=0): \psi(x,0)= \frac {2bx} {a} for 0<x<\frac {a} {2} and \psi(x,0)= 2b(1- \frac {x} {a} ) for \frac {a} {2} <x<a Now, I wish to find the wave function of a general time...

Consider a super cold gas tube (of, say, hydrogen), is the wave function of the gas different than at a higher temperature? How about for a lone electron within the gas?