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Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Oscillations In An LC Circuit

Oscillations In An LC Circuit

An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by

Forced Oscillations

Forced Oscillations

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

Damped Oscillations

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

Limits with Oscillating Discontinuities

Limits with Oscillating Discontinuities

An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...

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Related Experiment Video

Updated: Feb 11, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Anomalous Rabi Oscillations in Multilevel Quantum Systems.

B Y Chang¹, I R Sola², Vladimir S Malinovsky³

¹School of Chemistry (BK21), Seoul National University, Seoul 08826, Republic of Korea.

Physical Review Letters

|April 26, 2018

Summary

Strong laser pulses cause excitation probability to oscillate at a frequency set by energy difference, not pulse area. This quantum dynamics phenomenon is useful for nonlinear spectroscopy and quantum state preparation.

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Area of Science:

Quantum optics
Atomic physics
Spectroscopy

Background:

Manifold of quantum states are typically described by complex energy level structures.
Rabi oscillations are fundamental to understanding the interaction of light with matter, particularly in quantum systems.

Purpose of the Study:

To investigate the behavior of excitation probability in a manifold of quantum levels under strong laser pulse excitation.
To determine the factors governing Rabi oscillation frequency in such systems.

Main Methods:

Theoretical analysis of quantum state excitation dynamics.
Modeling of Rabi oscillations under strong pulse conditions within a manifold of levels.

Main Results:

Excitation probability exhibits Rabi oscillations, with frequency dictated by energy difference, not pulse area for strong pulses.
Population and coherence are confined to a two-level subsystem (initial and target states) even when Rabi frequencies exceed energy differences.

Conclusions:

The observed dynamics offer a new perspective on light-matter interactions in multi-level systems.
This phenomenon has potential applications in advanced nonlinear spectroscopy and precise quantum state preparation.