What is the energy scale of a Hamiltonian?
Answers
Answered by
0
The picture below shows, in a unified way, a selection of energy and length scales in fields across all of physics. Note that energy scales decrease as length scales increase: this is because of the quantum-mechanical relation ℓ=ℏc/E" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15.68px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ℓ=ℏc/Eℓ=ℏc/E between a length scale ℓ" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15.68px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ℓℓ and an energy scale E" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15.68px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">EE. Here ℏ" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15.68px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ℏℏ is Planck's constant and c" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15.68px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">cc is the speed of light. A useful approximate value is ℏc=200MeVfm" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15.68px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ℏc=200MeVfmℏc=200MeVfm. One intuitive translation of the formula ℓ=ℏc/E" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15.68px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ℓ=ℏc/Eℓ=ℏc/E is that a particle with rest energy E" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15.68px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">EE can't be confined to a region of space whose diameter is significantly less than ℓ" role="presentation" style="display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15.68px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ℓℓ. If you try, then there is enough uncertainty in energy and momentum to create particle-anti-particle pairs that tend to escape the spatial region to which you're trying to confine the
Answered by
0
What is the energy scale of a Hamiltonian?
❱ Total energy and Hamiltonian. A quantity which is frequently required is the overlap matrix defined by (7.3) The overlap matrix elements between the spherical-wave basis.
Similar questions