Guide Hydrogen-ion wave function

Free download. Book file PDF easily for everyone and every device. You can download and read online Hydrogen-ion wave function file PDF Book only if you are registered here. And also you can download or read online all Book PDF file that related with Hydrogen-ion wave function book. Happy reading Hydrogen-ion wave function Bookeveryone. Download file Free Book PDF Hydrogen-ion wave function at Complete PDF Library. This Book have some digital formats such us :paperbook, ebook, kindle, epub, fb2 and another formats. Here is The CompletePDF Book Library. It's free to register here to get Book file PDF Hydrogen-ion wave function Pocket Guide.
The Born-Oppenheimer Approximation
Contents:
  1. Wave function for the hydrogen molecular ion - IOPscience
  2. Solving The Hydrogen Molecule Cation Exactly
  3. Concise Articles, Tutorials & Primers on Science, Math & Technology
  4. Supplementary files

Wave function for the hydrogen molecular ion - IOPscience

Fingerprint hydrogen ions. Dirac equation. Wave functions. Ground state. Excited states.

Quantum Wavefunction - Quantum physics - Physics - Khan Academy

Journal of Chemical Physics , 12 , []. We note, first, that most nuclei are orders of magnitude heaver than an electron.

Solving The Hydrogen Molecule Cation Exactly

For the lightest nucleus, the proton,. This mass difference is large enough to have important physical consequences. Let us think classically about this mass difference first. That is, it will simply follow the heavy particle wherever it goes, and , it will move rapidly in response to the heavy particle motion. As an illustration of this phenomenon, consider the simple mechanical system pictured below:.

Concise Articles, Tutorials & Primers on Science, Math & Technology

Considering this as a classical system, we expect that the motion will be dominated by the large heavy particle, which is attached to a fixed wall by a spring. The small, light particle, which is attached to the heavy particle by a spring will simply follow the heavy particle and execute rapid oscillations around it. The figure below bottom panel illustrates this:. In this illustration, when the heavy particle moves even a tiny amount, the light particle executes many oscillations around the heavy particle. What we can conclude, therefore, is that we can approximately fix the position of the heavy particle and just allow the light particle to move around before we advance the heavy particle to its next position.

Supplementary files

Light particles, such as electrons, tend to have very diffuse, delocalized wave functions, while heavy particles, such as the nuclei, tend to have wave functions that are very localized about the classical positions. This is illustrated in the figure below:. Figure 1: Crude picture of matter.

Nuclear wave functions are shown above the axis, electronic wave functions are shown below. Thus, taking the idea of solving the electronic problem for fixed nuclear positions seriously, we can write the molecular wave function as.


  • Retinoids: Advances in Basic Research and Therapy.
  • Wave function for the hydrogen molecular ion.
  • Foundations of Supply-Side Economics. Theory and Evidence.
  • Windows 10 Primer: What to Expect from Microsofts New Operating System.
  • Introduction.
  • Quantum Mechanics.

This is not an exact wave function for the molecule but an approximate one. Hence, we call this the Born-Oppenheimer approximation to the wave function.

The total classical energy of the molecule is. Therefore, the total Hamiltonian of the molecule is. The details of these operators are not that important for this discussion. Let us consider how the electronic and nuclear kinetic energy operators act on the wave function. Fingerprint hydrogen ions.

Navigation menu

Dirac equation. Wave functions. Ground state. Excited states. Journal of Chemical Physics , 12 , [].


  1. Boards at Work: How Directors View their Roles and Responsibilities.
  2. Replay: The History of Video Games.
  3. Hydrogen molecule ion ( H2+ ) by quantum mechanics..
  4. The Feynman Lectures on Physics Vol. III Ch. The Hydrogen Atom and The Periodic Table!
  5. The Hydrogen Molecular Ion.
  6. Hiring People (Essentials).