Because there are many individuals in this Reddit who are learning physics for the first time, an effort was made to explicitly write out the mathematics in as much detail as possible. It is hoped that this material will be of assistance.
The quantization rule of de Broglie in the 1920s is not an arbitrary guess, and demonstrates the direct mathematical consequence of treating the electron as a standing matter wave. It is hoped that this posting provides minor assistance to those who are initiating modern physics and quantum mechanics for the first time.
Physics is strictly distinct from pure mathematics.
Nevertheless, mathematical assistance is an essential prerequisite for a profound physical understanding.
I hope this material proves beneficial.
Physics is strictly distinct from pure mathematics.
Nevertheless, mathematical assistance is an essential prerequisite for a profound physical understanding. Therefore, I have endeavored to document these mathematical derivations with maximal detail.
I hope this material proves beneficial.
Angular momentum and spin typically appear in the middle of undergraduate quantum mechanics texts, which can be difficult to comprehend without a foundation in linear algebra. This post provides detailed algebraic derivations that are often omitted in standard texts. I hope this helps.
Matrix diagonalization in linear algebra is an exceptional discipline that significantly contributes to all engineering studies, including quantum mechanics.
I hope this helps.
This is my second post about angular momentum and spin in Quantum Mechanics.
It is a part of my lecture notes that I have organized over a long time.
If you read it slowly, anyone can fully understand it.
The topics are hard, but this is written easier and in more detail than any other book.
I hope this helps you a lot!
This text is written in detail so that learners studying quantum mechanics for the first time can understand the mathematical derivation processes at the undergraduate level.
Physics is not mathematics.
However, in quantum mechanics, while the language of mathematics is very important, understanding the physical reality is considered essential.
While graduate-level textbooks typically begin with the Stern-Gerlach experiment, this undergraduate approach commences with the mathematical background underlying Planck's quantum hypothesis.
Even if you fall again, rise up and try once more. It’s our DNA.
This text is described in detail so that learners studying quantum mechanics for the first time can understand the mathematical derivation processes at the undergraduate level.
Physics is not mathematics.
However, in quantum mechanics, while the language of mathematics is very important, understanding the physical reality is considered the most important.
Even if you fall again, rise up and try once more. It’s our DNA.
For students of linear algebra and mathematical physics, moving from continuous wavefunctions to abstract operator algebra often feels like a huge, confusing gap.
In this post, I demonstrate the complete, step-by-step derivation of how the spherical Laplacian organically decomposes into angular momentum operators.
By stripping away the mathematical ambiguity, this excerpt shows exactly how spatial gradients and variable separation directly give birth to the discrete eigenvalues and Dirac ket notation |l, m⟩.
My goal is to make the complex algebra clear and simple for everyone. Good luck!
This post begins with the foundations of mathematical physics for students learning quantum mechanical angular momentum for the first time.
I believe that providing a more detailed mathematical approach over one or two additional pages can offer hope to a broader range of learners.
I have organized these notes to strip away the shell of complex symbols using the language of linear algebra, aiming to translate the underlying physical reality into a level of common sense that anyone can understand.
Good luck!
This post introduces the foundational topic regarding the emergence of quantum theory in modern physics and quantum mechanics. Based on my extensive experience instructing students, I have observed that many learners experience conceptual confusion and that existing texts fundamentally lack mathematical rigor. Therefore, I have newly reorganized the educational materials to address these issues.
Please note that this material consists entirely of text without illustrative diagrams. The rationale is that while learners are generally familiar with the standard diagrams, they often lack a profound understanding of the detailed theoretical explanations concerning the blackbody itself. Please understand that many visual diagrams have been intentionally omitted because the focus is strictly on providing these detailed textual explanations.
Even if you fall again, rise up and try once more. It's our DNA.
For learners encountering blackbody radiation for the first time in quantum mechanics, let us now achieve a perfect understanding. Through rigorous mathematical formulas and physical interpretations, you can verify the dawn of quantum theory in the early 1900s.
Even if you fall again, rise up and try once more. It’s our DNA.
This post is an excerpt from my long-standing lecture materials. While many textbooks merely present the tables and skip the detailed derivations, I am sharing this section for curious learners.
I hope this material will be a great help.
Utilizing Paul Dirac's elegant algebraic approach, this post presents the concept of spin through accessible and detailed examples.
This material will be a great help for both academic examinations and the comprehension of modern quantum information science.
This post introduces the concept of the spin-1/2 state and accessible examples, which are also highly beneficial for quantum information. I hope this aids your learning.
This post covers the rigorous mathematical derivation of Clebsch-Gordan coefficients utilizing ladder operators.
I hope this material proves helpful to your studies.
By Taeryeon.
This post provides an understanding of the concept of spin angular momentum based on linear algebra operators through examples.
The attached images detail the mathematical formulation of a spin-1/2 state. The contents encompass:
⋅ Definition of eigenstates utilizing Dirac notation.
⋅ Derivation of Pauli spin matrices.
⋅ Application of ladder operators.
⋅ Calculation of eigenvalues and measurement probabilities for for Ŝ_x, Ŝ_y, and Ŝ_z operators.
I hope this material helps your study. By Taeryeon.
This material is the third post regarding angular momentum and spin in Quantum Mechanics.
In the rapidly changing quantum era of 2026, the ambiguous concepts and implicit texts of 30 to 40 years ago must be replaced with concise concepts and explicit mathematical examples.
Consequently, texts that help academic growth and rapid adaptation to respective field are demanded.
I hope this material helps your study. By Taeryeon.
This material is the third posting concerning angular momentum and spin.
In the era of quantum computing, the conventional quantum mechanics of the past 30 to 40 years must be easily learnable.
To bridge undergraduate and graduate programs, this material serves as a universally comprehensible textbook providing detailed concepts and explicit mathematical examples based on linear algebra.
Verify this directly through this posting. By Taeryeon.