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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.

The Dot Product

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Measuring how one directional quantity affects another along a specific path involves comparing their orientation and strength. When two such quantities are represented using direction and amount, a numerical result is computed to show how much one acts along the path of the other. This result comes from a rule combining both inputs' horizontal and vertical parts and adding the results.This calculation gives a single value that grows larger when both inputs point in similar directions and...

Dot Product

Dot Product

The dot product is an essential concept in mathematics and physics.
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
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Dot Product: Problem Solving

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The dot product is a powerful tool in problem-solving involving vectors, given that the dot product of two vectors is the product of their magnitudes and the cosine of the angle between them measured anti-clockwise. Solving problems involving the dot product requires understanding its properties and developing a step-by-step process to solve them. Here are the main steps to follow when solving any general problem involving the dot product:
Identify the problem: Start by reading the problem and...

Scalar Product (Dot Product)

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The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a number, that is, a scalar quantity. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
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Related Experiment Video

Updated: Feb 14, 2026

Production and Targeting of Monovalent Quantum Dots

Production and Targeting of Monovalent Quantum Dots

Published on: October 23, 2014

Transparent Displays Utilizing Nanopatterned Quantum Dot Films.

Sang-Ho Shin^1,2, Boyeon Hwang¹, Zhi-Jun Zhao²

¹Department of Electrical Engineering, College of Engineering, Korea University, Seoul, 02841, Korea.

Scientific Reports

|February 8, 2018

Summary

This summary is machine-generated.

Researchers developed a transparent display using a nanopatterned quantum dot (QD) film. This novel quantum dot display offers excellent transmittance and wide viewing angles for vibrant image generation.

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Area of Science:

Materials Science
Optoelectronics
Nanotechnology

Background:

Transparent displays are crucial for augmented reality and advanced visualization.
Existing technologies often face limitations in transmittance, viewing angle, or fabrication scalability.
Quantum dots (QDs) offer tunable light emission properties suitable for display applications.

Purpose of the Study:

To realize a high-performance transparent display utilizing nanopatterned quantum dot films.
To investigate the feasibility of using nanoimprint lithography and spin coating for QD film fabrication.
To demonstrate active image generation with color modulation on a transparent substrate.

Main Methods:

Fabrication of a nanopatterned quantum dot film via nanoimprint lithography (NIL) and spin coating of colloidal QDs.
Attachment of the QD film to transparent glass.
Active image generation using a specific wavelength laser excitation.
Characterization of transmittance, viewing angles, and image quality.

Main Results:

Achieved a transparent display with a nanopatterned quantum dot film exhibiting high transmittance (>80%).
Demonstrated selective light emission and color modulation by controlling QD layer via nanopatterning.
Confirmed wide viewing angles and effective image realization in both bright and dark environments.
Established a simple and scalable fabrication process applicable to large areas.

Conclusions:

The developed nanopatterned QD film is a viable technology for creating high-quality transparent displays.
The fabrication method is simple, scalable, and suitable for large-area manufacturing.
This technology opens possibilities for advanced transparent display applications in various fields.