Basics of Quantum Mechanics

Chapter 1: Introduction to Quantum Mechanics

1.1 What is Quantum Mechanics?

Quantum mechanics is the branch of physics that studies the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles.

1.2 Why is Quantum Mechanics necessary?

Classical mechanics, which describes the behavior of macroscopic objects, cannot be applied to the smallest scales. This is because the laws of classical mechanics break down at the atomic and subatomic level.

1.3 The Wave-Particle Duality

One of the key concepts in quantum mechanics is the wave-particle duality, which states that all matter and energy exhibits both wave-like and particle-like behavior.

Chapter 2: The Schrödinger Equation

2.1 What is the Schrödinger Equation?

The Schrödinger equation is a mathematical formula that describes the behavior of quantum systems. It determines the probability distribution of the position and momentum of a particle.

2.2 How to solve the Schrödinger Equation

Solving the Schrödinger equation is a complex task and requires advanced mathematical techniques. However, for simple systems, analytical solutions can be found.

2.3 Interpretation of the Schrödinger Equation

The solution to the Schrödinger equation gives the wave function of a quantum system, which provides information about the probabilities of finding the particle in certain positions and with certain momenta.

Chapter 3: Quantum States and Operators

3.1 What are Quantum States?

Quantum states are the possible conditions that a quantum system can be in. They are represented by wave functions, which describe the probabilities of finding the particle in certain positions and with certain momenta.

3.2 What are Operators in Quantum Mechanics?

Operators are mathematical objects that act on quantum states. They can be used to describe physical quantities, such as position and momentum, and to make predictions about the behavior of quantum systems.

3.3 Hermitian Operators and Eigenvalues

Hermitian operators are a special type of operator that have real eigenvalues. The eigenvalues of a Hermitian operator represent the possible values that a physical quantity can have in a quantum system.

Chapter 4: Quantum Mechanics of Systems with Spin

4.1 What is Spin?

Spin is a intrinsic property of subatomic particles that behaves like a tiny bar magnet. It is an important concept in quantum mechanics, as it gives rise to many of the phenomena observed in atomic and subatomic systems.

4.2 Spin angular momentum and its operators

Spin angular momentum is a measure of the intrinsic angular momentum of a particle. It is described by spin angular momentum operators, which act on the spin states of the particle.

4.3 Stern-Gerlach Experiment

The Stern-Gerlach experiment is a classic demonstration of the quantization of angular momentum in quantum mechanics. It shows that particles with spin have a definite angular momentum and can only have certain values of that angular momentum.

Chapter 5: Quantum Mechanics of Systems with Multiple Particles

5.1 What is the Pauli Exclusion Principle?

The Pauli exclusion principle states that no two identical fermions (particles with half-integer spin) can occupy the same quantum state simultaneously. This principle has far-reaching consequences and is one of the cornerstones of quantum mechanics.

5.2 Identical Particles and Symmetrization

In systems with multiple identical particles, the wave function must be properly symmetrized or antisymmetrized to take into account the indistinguishability of the particles. This is important for calculating the probabilities of finding the particles in certain configurations.

5.3 The Two-Particle Schrödinger Equation

The Schrödinger equation can be generalized to describe systems with multiple particles. The two-particle Schrödinger equation is a particular case that is useful for understanding the behavior of systems with two particles.

Chapter 6: The Hydrogen Atom

6.1 Introduction to the Hydrogen Atom

The hydrogen atom is a simple system that consists of a single electron orbiting a nucleus with a single proton. It is one of the most well-studied systems in quantum mechanics and serves as a useful example for understanding many of the concepts introduced earlier.

6.2 The Hydrogen Atom Wave Functions

The wave functions for the hydrogen atom can be obtained by solving the Schrödinger equation. They describe the probability distribution of the electron in the hydrogen atom and are used to calculate various physical properties, such as the energy levels and the spectroscopic lines.

6.3 The Hydrogen Atom Energy Levels

The energy levels of the hydrogen atom are determined by the wave functions and are characterized by the principal quantum number, n. The energy levels have important consequences for the behavior of the hydrogen atom, including its stability and the spectroscopic lines that it emits.

Chapter 7: Quantum Mechanics of Systems with Continuous Variables

7.1 What are Continuous Variables?

Continuous variables are physical quantities, such as position and momentum, that can take on any value within a certain range. In contrast, discrete variables can only take on a limited set of values.

7.2 The Position Representation and the Momentum Representation

The position representation and the momentum representation are two different ways of describing the same quantum state. They are related to each other by the Fourier transform and provide complementary information about the particle.

7.3 The Uncertainty Principle

The uncertainty principle is a fundamental concept in quantum mechanics that states that it is impossible to simultaneously determine the position and momentum of a particle with arbitrary precision. The uncertainty principle is a direct consequence of the wave-particle duality and has important implications for the behavior of quantum systems.

This is a general overview of the basics of quantum mechanics. Of course, there is much more to learn and explore in this fascinating field of physics, but this should provide a good starting point for further study.

Comments

Krishna ki chetawani -- कृष्ण की चेतावनी

कृष्ण की चेतावनी -- रामधारी सिंह दिनकर वर्षों तक वन में घूम घूम बाधा विघ्नों को चूम चूम सह धूप घाम पानी पत्थर पांडव आये कुछ और निखर सौभाग्य न सब दिन सोता है देखें आगे क्या होता है मैत्री की राह दिखाने को सब को सुमार्ग पर लाने को दुर्योधन को समझाने को भीषण विध्वंस बचाने को भगवान हस्तिनापुर आए पांडव का संदेशा लाये दो न्याय अगर तो आधा दो पर इसमें भी यदि बाधा हो तो दे दो केवल पाँच ग्राम रखो अपनी धरती तमाम हम वहीँ खुशी से खायेंगे परिजन पे असी ना उठाएंगे दुर्योधन वह भी दे ना सका आशीष समाज की ले न सका उलटे हरि को बाँधने चला जो था असाध्य साधने चला जब नाश मनुज पर छाता है पहले विवेक मर जाता है हरि ने भीषण हुँकार किया अपना स्वरूप विस्तार किया डगमग डगमग दिग्गज डोले भगवान कुपित हो कर बोले जंजीर बढ़ा कर साध मुझे हां हां दुर्योधन बाँध मुझे ये देख गगन मुझमे लय है ये देख पवन मुझमे लय है मुझमे विलीन झंकार सकल मुझमे लय है संसार सकल अमरत्व फूलता है मुझमे संहार झूलता है मुझमे उदयाचल मेरा दीप्त भाल, भूमंडल वक्षस्थल विशाल, भुज परिधि-बन्ध को घेरे हैं, मैनाक-मेरु पग मेरे हैं। दिपते जो ग्रह नक्षत्र निकर, सब हैं

आ तमाशा तू भी देख

देखने वाले देखते हैं, सब कुछ देखते हैं ये लोग देख देख कुछ करते नहीं, जाने कहाँ से लगा ये रोग । गरीब देखा, पीड़ित देखा, देखे उनके खेत बंजर फर्क उनको कुछ पड़ा नहीं, देख किसानों का ये मंजर झूठ वादा, झूठे काम, किसानों के प्रति झूठा सम्मान सब देख मंद मुस्काते हैं, चाहे फांद गला लटके किसान हिन्दू देखा, मुस्लिम देखा, देखी जाने कितनी जाती पर जिससे इंसान दिखें, ऐसी कला कहाँ उनको आती देखने वाले देखते हैं, सब कुछ देखते हैं ये लोग देख देख कुछ करते नहीं, जाने कहाँ से लगा ये रोग । घर में देखा, ऑफिस में देखा, देखा ओलंपिक्स में परचम लहराते चाहे जितने हुनर उनके देखे, पर कसी फब्तियां आते जाते कल के दुश्मन आज हैं भाई, गले पड़े भुला के सब लफड़े लेकर ठेका आदर्शवाद का, नाप रहे दूजों के कपडे अधरों पे बेशर्मी का पर्दा, जो पीड़ित है उसी की गलती देख देख इन बड़बोलों को, दानवों की कमी कहाँ है खलती देखने वाले देखते हैं, सब कुछ देखते हैं ये लोग देख देख कुछ करते नहीं, जाने कहाँ से लगा ये रोग । सड़क नहीं, बिजली नहीं, जनता का पैसा, उनकी जेब जहाँ देखो वहीँ मिलेंगे, भरे प

Mahabharat

प्रेम व प्रथम विवाह प्रेम व प्रथम... प्रेम व विवाह प्रेम व विवाह शान्तनु शान्तनु गंगा गंगा देवव्रत देवव्रत past encounter past encounter सत्यवती सत्यवती ऋषि परासर ऋषि परासर वेद व्यास वेद व्यास आठवाँ पुत्र आठवाँ पुत्र प्रथम ७ पुत्रों को नदी में बहाया प्रथम ७ पुत्रों को नदी में बहाया पुत्र पुत्र विवाह पूर्व पुत्र विवाह पूर्व पुत्र पुत्री पुत्री दासराज दासराज पुत्र पुत्र पुत्र पुत्र संतान संतान चित्रांग्ध चित्रांग्ध विवाह विवाह विवाह विवाह विचित्रविर्य विचित्रविर्य विवाह को तिरस्कार किया विवाह को तिरस्कार किया प्रेमी प्रेमी अम्बा अम्बा अंबिका अंबिका loses her color on seeing vyas loses her color... अम्बालिका अम्बालिका तिरस्कार किया तिरस्कार किया शाल्व्य शाल्व्य विवाह विवाह गोद ले लिया गोद ले लिया गांधारी की दासी से पुत्र गांधारी की दासी से पुत्र धृतराष्ट्र धृतराष्ट्र प्रथम पुत्र(जन्म से अंधा) प्रथम पुत्र(जन्म से अंधा) नियोग क्रिया नियोग क्रिया पुत्र पुत्र नियोग क्रिया नियोग क्रिया विवाह विवाह विवाह विवाह पांडु पांडु अंबि

Morse Code Tree

Morse Code Morse Code E E I I S S H H A A R R U U L L F F V V T T M M O O N N B B D D Y Y K K X X C C Z Z G G Q Q Dot Dot Dash Dash Text is not SVG - cannot display

BCCI fails to renew domain name for its official website

www.bcci.tv is(or should I use "was") the BCCI's official website where it posts news about Indian cricket and even live-stream the cricket events. I tried to reach to their page and it's rendering above page as the domain has expired and BCCI(Board of Control for Cricket in India) has failed to renew it within the expiry deadline. After using whois for this domain name, I got to know that the domain was registered on 2nd February 2006 and was updated again today on 4th February 2018. Will BCCI be able to regain its domain back? Update : BCCI has got its domain back and showing the contents as earlier.

कोई तो होता

भटकता जब मैं अपना पथ भूल जाता लगाकर मैं गोता, वापस मुझको लाने वाला काश ऐसा कोई तो होता। गिरकर, भटककर, खाकर चोट जब मैं मन ही मन रोता, मेरे दुखों को समझने वाला काश ऐसा कोई तो होता। सन्नाटे के धुंध में जब चुप चुप अकेले मैं सोता, मुझसे बातें करने वाला काश ऐसा कोई तो होता। अनगिनत जिम्मेदारियां अपनी होकर असहाय जब मैं ढोता, मुझको सहारा देने वाला काश ऐसा कोई तो होता। जीवन के संघर्षों से लड़कर जब मैं अपना मनोबल खोता, साहस मुझे बंधाने वाला काश ऐसा कोई तो होता। खाकर अपने पीठ पे खंजर जब मैं अपने जख्मों को धोता, मरहम मुझको करने वाला काश ऐसा कोई तो होता। -- शशिकांत * उपरोक्त पंक्तियाँ मेरी पुस्तक " आ तमाशा तू भी देख " का अंश हैं।

[Fixed] Alexa can count only from 1 to 10

Note : At the time of writing this post, Alexa had this issue which has been resolved. Alexa can now count flawlessley even in reverse. Alexa is the smart virtual assistance by Amazon. It is beating google now and Siri on non-screen devices. Alexa is hailed for its intelligence but it seems that the Alexa knows to count only from 1 to 10. By 1 to 10, I mean exactly from 1 to 10; neither more nor less. Even asking Alexa to count from 1 to 5 or 3 to 10 or 3 to 5 results in an apology from Alexa. Watch the above video to see for yourself.

JSON vs YAML

JSON JSON(JavaScript Object Notation) is a human-readable data exchange format. JSON is built on two structures: A collection of name/value pairs. In various languages, this is realized as an object, record, struct, dictionary, hash table, keyed list, or associative array. An ordered list of values. In most languages, this is realized as an array, vector, list, or sequence. JSON's basic data types are: Number : a signed decimal number that may contain a fractional part and may use exponential E notation, but cannot include non-numbers such as NaN. The format makes no distinction between integer and floating-point. JavaScript uses a double-precision floating-point format for all its numeric values, but other languages implementing JSON may encode numbers differently. String : a sequence of zero or more Unicode characters. Strings are delimited with double-quotation marks and support a backslash escaping syntax. Boolean : either of the values true or false Arra

Tenhash Post

Search Tenhash Post