The World Of Quantum Mechanics

    The World Of Quantum Mechanic

"Those who are not shocked when they first come across quantum theory cannot possibly have understood it." - Niels Bohr

1.            Introduction:

Quantum mechanics is totally a different field of science filled with lots of maths, uncommon things and mind blowing phenomena. The word quantum means 'the smallest unit' of some particular physical objects or properties like energy for instance.It is one of the most powerful subject of physics due to its vast and enormous applications in the modern digital, medical, astronomy, almost everywhere and i will tell you later on how .

2.     What actually is quantum mechanics?

"In the simplest terms, quantum mechanics is a branch of physics in which we study about the wave-particle dual nature of microscopic particles and their dynamics".

I know it's quite fuzzy to get it but don't worry i will simplify this explanation as much as possible.

I am going to explain the basic concepts and principles of quantum mechanics in relation to classical mechanics as well so that you actually get a feel to grasp it.

So first of all let me explain you classical mechanics in short and concise way:

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Classical mechanics is the branch of physics that describes the motion of macroscopic objects under the influence of forces/dynamics. It applies to systems ranging from planets,stars and projectiles to everyday objects, provided they move at speeds much slower than light and are not at atomic or subatomic scales which requires other description.

Classical mechanics is based on the following fundamental concepts and principles:

1.Determinism:

The future of an event can be completely determined if its initial conditions (position, velocity,time,etc.) are given.

2.Newton's laws of motion:

There are three Newton's laws of motion but the 2nd one is most fundamental cuz it explains the dynamics of particles using this equation:

credit: image

Where,

F=force

m=mass

a=acceleration 

3.Conservation laws:

If there is nothing to disturb the system then certain quantities like energy and momentum are conserved.

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Now I am going to explain quantum mechanics in the similar fashion:

As i have already defined quantum mechanics above,i am simply explaining its basic mathematical concepts and principles:

1.Wave-particle duality:

All quantum particles exhibit both particle nature as well as wave nature depending on physical situations(experiment, interaction,etc.)

2.Wave functions:

Quantum particles are described by the wave function which measures the probability of finding a particle within a finite region.

3.Superposition:

A particle exists in a superposition of states which means (in a simple particular terms) a particle can exists in two or more different places at the same time. Isn't it making you feel shocked? Of course it does!

Mathematically it also means that a linear combination of different wave functions(solutions of Schrodinger equation)  is another wave function which is a solution of Schrodinger equation.

4.Schrodinger equation:

Just as Newton's force equation governs the dynamics of the system,the Schrodinger equation governs the dynamics of the quantum system (particles).This equation is of the form of "heat equation" which is a partial differential equation. The Schrodinger equation looks as follow:

credit:  image

3.       History of quantum mechanics:

The idea of quantum mechanics  originated gradually around 1900 when there were disagreement among thousands of experimental results on electromagnetic radiation and wave nature of light such as photoelectric effect experiment, black body radiation. It was pretty well clear that light exhibits wave nature as shown by the Young's double slit experiment but it was also experimentally found that it light possess particle nature in experiments like photoelectric effects.

I am giving short introductory information about the history of quantum mechanics.

Quantum mechanics emerged in the early 20th century to address phenomena classical physics could not explain. Its inception is marked by Max Planck's 1900 proposal of energy quantization to resolve blackbody radiation issues. Albert Einstein further advanced this in 1905 with his explanation of the photoelectric effect, establishing light's particle nature. 

The theory evolved through contributions from Niels Bohr, Werner Heisenberg, and Erwin Schrödinger in the 1920s, leading to the formalization of quantum mechanics as we know it today, including wave mechanics and matrix mechanics which explains the quantum mechanical phenomena like tunneling, superposition, entanglement in different mathematical frameworks. 

4.        Why quantum mechanics?

Quantum mechanics stands at the very foundation of modern physics, offering a framework to understand the universe at its most fundamental level. Unlike classical physics, which excels in describing macroscopic phenomena, quantum mechanics reveals the rules governing the microscopic world—atoms, electrons, and photons.

But why should we care about quantum mechanics and why it is so important part of science?

1. Revolutionary Insight:

Quantum mechanics challenges our intuitive understanding of reality. It introduces concepts like wave-particle duality, superposition, and entanglement, which defy classical logic. These ideas not only expand our understanding of nature but also push the boundaries of human imagination.

2. Technological Advancement:

Quantum mechanics is not just a theoretical construct; it has led to numerous practical applications that shape our daily lives:

(A).   Electronics: 

The principles of quantum mechanics are foundational for semiconductors and transistors, which are crucial for all modern electronic devices.

(B).   Medical Imaging: 

Technologies like Magnetic Resonance Imaging (MRI) utilize quantum principles to provide detailed images of internal organs without invasive procedures.

(C).   Lasers: 

Quantum mechanics explains how lasers work by stimulating atoms to emit light coherently, leading to applications ranging from barcode scanners to advanced surgical tools.

(D).    Quantum Computing:

 This emerging technology promises to revolutionize computing by solving complex problems much faster than classical computers through the use of qubits based on the superposition principle of quantum mechanics.

3. Fundamental Curiosity:

At its core, quantum mechanics addresses questions about the nature of existence. Why do particles behave the way they do? What lies beneath the probabilistic nature of quantum phenomena? Exploring quantum mechanics is akin to seeking answers to the universe's deepest mysteries.

4. Bridging the Gaps:

Quantum mechanics plays a crucial role in unifying physics. It serves as the foundation of quantum field theory, the framework for understanding fundamental particles and forces. 

5. Beauty in Complexity:

Beyond its practical implications, quantum mechanics is a testament to the elegance of mathematics and the power of human thought. The equations of quantum mechanics—such as Schrödinger's equation and Heisenberg's uncertainty principle—beautifully encapsulate the strange yet harmonious dance of particles and waves.

Whether you're driven by intellectual curiosity, the quest for technological progress, or the sheer awe of understanding the universe, quantum mechanics offers a gateway to explore the infinite possibilities of science.

5.     How to learn quantum mechanics?

Learning quantum mechanics is bit more tricky. If you follow the right approach then you can learn the basic mathematical formalism in an easy and short way if your background in physics and mathematics especially calculus is robust.

If you are high school student then it might be little bit difficult to learn quantum mechanics (specifically its mathematical formalism) but don't worry I have written another very detailed blog on how to learn quantum mechanics from basic to advance level provided that you are hardworking and passionate about it.

Here is the link to that blog : Link

You don't need to read every topics of this blog,you just need to read points 4 and 6.

If you are from other background like biology, chemistry or mathematics (suppose you are college students who doesn't have physics major) then you shouldn't go into much detail and the difficult mathematical parts.

Here are some of the best books that you can read and understand basics of quantum mechanics without going through the mathematical formalism:

1.How to Teach Quantum Physics to Your Dog" by Chad Orzel

2. Quantum Physics for Beginners in 90 Minutes without Math

6.    Why is quantum mechanics so weird?

No one understands quantum mechanics?

It's quite often said that no one understands quantum mechanics,the question is why and how? Did you ever try to explore this statement?

Quantum mechanics is just a mathematical theory or model to understand the subatomic/microscopic phenomena and the fact that the most of the quantum mechanical phenomena are beyond the understanding level of people like me and you,this makes quantum mechanics really so weird that even Richard Feynman told us that "no one understands quantum mechanics" and that's when this statement became quite popular.

I will explain this statement with a famous example of double slit experiment .

The double-slit experiment is one of the most fascinating demonstrations of quantum mechanics because it highlights the dual nature of particles and the role of measurement. Here's a step-by-step explanation of its significance and the explanation of "weirdness" of quantum mechanics:

            **The Double Slit Experiment**

*Setup:

A source(electron gun) that emits stream of particles (electrons) toward a barrier with two slits.

Beyond the barrier is a screen that records the particle impacts and the interference patterns are shown on it. The experimental setup with different apparatus are shown below:

Credit:image

*Classical Expectation:

If particles were purely particles (like bullets), we would expect to see two distinct bands on the screen, corresponding to the slits cuz there are only two slits (a small gap in the sheet).The two bands produced on the screen are shown below:

*What Actually Happens?

When no one observes which slit the particle goes through, the particles create an interference pattern (a series of bright and dark fringes) on the screen. This pattern is characteristic of waves, not particles.The interference patterns produced are shown below: 

Credit: Click on the link image

               The Quantum "Weirdness"

1.Wave-Particle Duality

Each particle seems to act like a wave when going through both slits simultaneously and interfering with itself.

However, when you try to measure which slit the particle passes through, the interference pattern disappears, and the particles behave like particles, creating only two distinct bands on the screen.

2.Conclusion from experiment:

The particle's behavior changes depending on whether it is being observed.

It exists in a superposition of states (going through both slits) until observed. That's where weirdness of quantum mechanics comes into picture.

Initially you must have expected that there will be only two bands on the screen as there are only two slits.But when the electrons pass through these two slits and due to some quantum phenomenon,they actually produce more than two different bands on the screen(It's like you drop some sands through two holes in a sheet and you see only two bands behind the hole and now think what happens when there is actually more than two bands ?). Isn't it weird? 

So the question is how can we explain this phenomenon in which even particles show interference phenomenon? It turns out that the explanation is given by quantum mechanics!

        Explanation by quantum mechanics.     

Quantum mechanics explains the formation of electron interference patterns in the following way:

•Particles have dual nature and so the electrons being a particle exhibit wave nature to show interference patterns.

•Particles don't follow classical trajectories.Instead, they exist in a superposition of all possible paths(paths available through two slits).

•When observed or detected through eyes or detector, the electron appears as a localized particle at a single point on the screen.

•An electron is described a wave function which measures the probability of finding an electron at a specific region.When the electron passes through the two slits(in the form of wave),the wavefunction splits into two parts, one passing through each slit.

These parts interfere with each other, leading to constructive and destructive interference, which forms the characteristic fringe pattern on the detection screen.

That's how interference patterns with maxima and minima(bright and dark) are formed on the screen.

Thank you for reading!

Author: Scientificirfan 

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