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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

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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. Schrödinger...

Calculation of First-Law Quantities II

Calculation of First-Law Quantities II

The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...

Calculation of First Law Quantities I

Calculation of First Law Quantities I

Thermodynamic systems undergoing phase transitions or temperature changes experience energy transfer in the form of heat (q) and work (w). For a reversible phase change at constant temperature (T) and pressure (p), the process involves no chemical reaction but results in energy exchange between distinct phases.The heat transferred during this process corresponds to the latent heat of transition, which is the amount of heat energy absorbed or released by a substance when it changes from one...

Base Quantities and Derived Quantities

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In any system of units, the units for some physical quantities must be specified through a measurement process. These measurements are the base quantities of the system, and their units are the base units of the system. The algebraic combinations of the base values can then be used to express all other physical quantities. Each of these physical quantities is then referred to as a derived quantity, with each unit being referred to as a derived unit.
The International Organization for...

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On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...

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Related Experiment Video

Updated: Jun 5, 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

Modular values and weak values of quantum observables.

Y Kedem¹, L Vaidman

¹Raymond and Beverly Sackler School of Physics and Astronomy Tel-Aviv University, Tel-Aviv 69978, Israel.

Physical Review Letters

|January 15, 2011

Summary

This summary is machine-generated.

A new modular value concept for quantum systems is introduced, applicable to any coupling strength with qubit meters. This framework explains current experimental findings in quantum measurements.

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

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Area of Science:

Quantum mechanics
Quantum information theory
Measurement theory

Background:

Pre- and postselection in quantum mechanics allows for unique measurement conditions.
Weak values offer insights into quantum systems but are limited to weak couplings.
Understanding quantum system interactions with measurement devices is crucial.

Purpose of the Study:

Introduce the concept of a modular value for pre- and postselected quantum systems.
Generalize this concept for composite systems and multiqubit meters.
Provide a theoretical explanation for recent experimental results in quantum measurements.

Main Methods:

Conceptual introduction of the modular value.
Mathematical formulation for coupling to qubit meters.
Extension to composite systems and multiqubit meters.

Main Results:

The modular value is defined for pre- and postselected quantum systems.
It relates to weak values but applies to arbitrary coupling strengths with qubit meters.
The generalized concept explains phenomena observed in current experiments.

Conclusions:

The modular value offers a new perspective on quantum measurements, particularly with qubit meters.
This concept extends the utility of quantum values beyond weak coupling regimes.
The framework successfully accounts for complex experimental observations in quantum systems.