Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Classical Physics
Quantum Physics
Quantum Interpretations
Special and General Relativity
Atomic and Condensed Matter
Nuclear and Particle Physics
Beyond the Standard Model
Cosmology
Astronomy and Astrophysics
Other Physics Topics
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Physics
Quantum Physics
Highly localized initial psi in harmonic well
Reply to thread
Message
[QUOTE="vanhees71, post: 5505677, member: 260864"] It will slosh around forever in a complicated way. You can just solve the equation of motion by using the well-known energy-eigenstates. Given the wave function ##\psi(t,\vec{x})## at ##t=0## you define the corresponding coefficients $$\psi_j=\int_{-\infty}^{\infty} u_j^*(x) \psi(0,\vec{x}),$$ where ##u_j(x)## is the energy eigenfunction with eigenvalue ##E_j=(j+1/2)\omega##, ##j \in \{0,1,2,\ldots \}##. Then the wave function at any later time is given by $$\psi(t,x)=\sum_{j=0}^{\infty} \exp(-\mathrm{i} E_j t) \psi_j u_j(x).$$ This immediately shows that you never converge to an energy eigenfunction but that for any time all components of the initial wave function stay involved. This must be so, because only the energy eigenfunctions represent stationary states, i.e., if initially you don't have the system prepared in an energy eigenfunction the state can never become an energy eigenstate later. [/QUOTE]
Insert quotes…
Post reply
Forums
Physics
Quantum Physics
Highly localized initial psi in harmonic well
Back
Top