Quantum Mechanics series 🔥 Lecture 03
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- เผยแพร่เมื่อ 15 ต.ค. 2024
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Very helpful for Ungrad Physics students 👍🏻
We want more
I am studying in class 11 , but i have studied modern physics more than a student of 12th , i have an interest toward modern physics , quantum theory , relativity , particle and high energy physics , the unsolved problem of quantum gravity ...... And an aptitude towards mathematics.....so i would request to please make a series of lectures starting from old quantum theory and linear algebra to Schrodinger equation , it's applications to many idealistic problems , and then of course into dirac formulation....and at last approximate methods and particle physics.
There are many physics enthusiasts like me who want to know modern physics deeply.
So please try to make a lecture series on it
A vector space is a concept in mathematics that helps us understand and work with vectors. Vectors are quantities that have both a size and a direction.
### 1. **Vectors:**
Think of vectors as arrows pointing in different directions. Each arrow has a certain length (size) and points in a specific direction. For example, you can have arrows on a piece of paper pointing in various directions.
### 2. **What is a Vector Space?**
A vector space is a collection of these arrows (vectors) where you can do two main things:
- **Add two vectors together:** If you add one arrow to another, you get a new arrow.
- **Multiply a vector by a number:** If you stretch or shrink an arrow by a number, you get a new arrow.
### 3. **Rules of a Vector Space:**
For a collection of vectors to be considered a vector space, it needs to follow these rules:
1. **Adding Vectors:** When you add two vectors, the result should still be a vector in the same space.
2. **Order of Adding Doesn't Matter:** Adding vectors in any order should give the same result.
3. **Zero Vector:** There should be a special vector, like an arrow with no length, that when added to any vector, leaves the vector unchanged.
4. **Opposite Vector:** For every vector, there should be another vector pointing in the opposite direction, so that adding them together gives the zero vector.
5. **Multiplying by Numbers:** If you multiply a vector by a number, the result should still be a vector in the same space.
6. **Distributing Multiplication Over Addition:** If you add two vectors and then multiply the result by a number, it should be the same as multiplying each vector by that number first and then adding them.
7. **Distributing Addition Over Multiplication:** If you multiply a vector by two different numbers separately and then add the results, it should be the same as adding the numbers first and then multiplying by the vector.
8. **Combining Multiplications:** If you multiply a vector by one number and then by another, it should be the same as multiplying by the product of the two numbers.
9. **Identity for Multiplication:** Multiplying a vector by one should leave the vector unchanged.
### 4. **Examples of Vector Spaces:**
- **Euclidean Space:** Imagine the arrows on a flat piece of paper or in three-dimensional space. These arrows form a vector space.
- **Polynomials:** Think of polynomial equations like \(x^2 + 2x + 3\). The set of all such polynomial equations forms a vector space.
- **Matrices:** These are grids of numbers arranged in rows and columns. The set of all such grids forms a vector space.
- **Functions:** Imagine a graph of a continuous function. The set of all such graphs forms a vector space.
### 5. **Basis and Dimension:**
- **Basis:** A basis is a set of vectors that you can use to create any vector in the space. These vectors are like building blocks.
- **Dimension:** The dimension of a vector space is the number of vectors in the basis. For example, in a 3-dimensional space, you need three vectors to describe any vector in that space.
### 6. **Subspaces:**
A subspace is a smaller collection of vectors within a vector space that is itself a vector space. It follows the same rules as the larger vector space.
### 7. **Linear Combinations, Span, and Linear Independence:**
- **Linear Combination:** A linear combination is when you add several vectors together, each multiplied by a number.
- **Span:** The span of a set of vectors is all the vectors you can create using linear combinations of those vectors.
- **Linear Independence:** Vectors are linearly independent if none of them can be written as a linear combination of the others.
### Summary:
A vector space is a collection of vectors where you can add vectors and multiply them by numbers, following specific rules. It’s a fundamental idea in mathematics that helps us understand and solve problems involving vectors. Understanding vector spaces is crucial for more advanced studies in math and science.
Maze aa gaye bhai saab ...the quantity and quality of the lecture is at its peak ..💥👑
Maza to abhi aur ayega :)
Bhaiya I have also made video's on Schrodinger equations and normalisation as 10 grader. 😀
Great lecture..
Really you teach quantum mechanics as. 10 grader?
Nice, bhejo link, dekhte hain :)
@@SciAstrath-cam.com/video/67mOPj_7u88/w-d-xo.htmlsi=9sJMNAKRKEOm4gTt
@@SciAstraThis is the link bhaiya.
Quantum tunneling is a fascinating concept from quantum mechanics, a branch of physics that deals with very small particles like electrons and protons.
### What is Quantum Tunneling?
Imagine you have a ball rolling towards a hill. In classical physics (the physics of everyday objects), if the ball doesn't have enough energy to climb over the hill, it will just roll back down. But in the quantum world, things are a bit different.
### The Quantum World
Particles like electrons don't behave exactly like balls. They have wave-like properties, meaning they can spread out and act like waves. This is known as wave-particle duality.
### The Tunnel Effect
When a tiny particle like an electron encounters a barrier (something that would be like the hill for the ball), it doesn't always bounce back. Instead, because of its wave-like nature, part of the electron's wave can actually go through the barrier, even if it doesn't have enough energy to get over it. This is called quantum tunneling.
### How It Works
1. **Wave Properties:** Think of the electron as a wave spreading out. When this wave hits the barrier, it doesn't stop completely. Part of the wave can continue on the other side of the barrier.
2. **Probability:** Quantum mechanics is all about probabilities. There is a small chance that the electron can be found on the other side of the barrier, even though classically it shouldn't be able to get there.
### Real-World Examples
Quantum tunneling isn't just a theoretical idea; it has real-world applications:
- **Sunshine:** The sun produces energy through nuclear fusion, a process that relies on quantum tunneling. Protons (particles in the nucleus of atoms) tunnel through the energy barrier that would normally keep them apart, allowing them to fuse and release energy.
- **Electronics:** Modern electronic devices like transistors rely on quantum tunneling. It helps electrons move through very thin barriers, allowing the devices to work efficiently.
- **Scanning Tunneling Microscopes (STM):** These microscopes use tunneling to create images of surfaces at the atomic level. By measuring the tunneling current, scientists can see the arrangement of individual atoms.
### Summary
Quantum tunneling is a phenomenon where tiny particles can pass through barriers that they wouldn't be able to cross according to classical physics. This happens because particles in the quantum world behave like waves and can spread out, giving them a chance to be found on the other side of the barrier. This concept is essential for many natural processes and modern technologies.
Thankyou!!!😍🤩
You’re welcome 😊
2:58 are 😅 bhaiya i² =-1
Yes. Galti se mistake 🥲
@Sciastra from when should we start preparation for NEST from 11th or 12th ??? Pls tell
Sir, My rank is in the round 1 of IAT but still I haven't gotten any admission offers‽ Suggest me what to do... or where to check? 🙏🏻🙏🏻🙏🏻
what is your rank?
Bhaiya I have a doubt
Universe toh infinite hai yani potential energy variable hai kabhi nikali ni ja skti
Constant tbhi hogi jab universe finite hoga
Ham par toh plancks bhi gravitation laga rhe honge and abhi toh ham jaante bhi nhi ki sbse smallest thing kya hai isliye smallest and largest infinity tk chlega that's why potential energy is
Not a constant it is variable and not defined
Ek object ke perspective se nikali gayi potential energy toh defined hogi but is universe ke har object and massy thing ke respect se nikali gayi potential energy not defined hogi
Bhaiya kya m sahi keh rha hu btao please.
I like that when bhaiya said "agr qm m life asan bnani h too " ye dirac notation pdna h😂
Han wo to karna padega na bhidu :)
@@SciAstra haha😆😂 btw , thank you bhaiya , I like the course . Mene phle qm ka ek course follow kia tha , around 10 videos ka hc verma sir ka , abhi too I am in 11 bhot zyada high level ka maths nhi aata. , too jb sir pdha rhe the to adhi cheeze dimag k upar s ja rhi thi . Comparatively apki videos ko m 70 percent to absorb kr par hi hu😉
😭😭 Thanks Bhaiya
You are most welcome :)
Bhaiya jayant Narlikar ji ki theory pa video baneya pls
banate hain :)
Good lecture 🎉
glad it was helpful...keep watching and please share!
Sagar bhaiya is still studying bs-ms in berhampur ane providing this. Imagine after phd 🔥
After PhD, he will teach you everything you are taught in your BS-MS haha.
@@SciAstra 🤩
@@SciAstra yes please
We will wait for that ...❤️❤️❤️
Imagine the level that bhaiya being got taught at iiser
Hello bhaiya maine kal saf payment kiya tha magar pin galat ho Gaya hai
Uske bad jab fhir se payment karne k lia try kiya to error show kar raha hai Maine jac ko mail kiya hai magar koi amswer nehi aya
Please bhaiya payment fhir se hoga ki nehi please bata do
Bhaiya is thus really true that electron moves around nuclues at constant mag. Of velocity . And also it radiates energy around nucleus.
Please answer i want deep answer of this question not what we taught in Bohr model..
Your question is incorrect. How is it that the atom revolves around the nucleus, because an atom itself contains the nuclei.
@@SciAstra ooo sory i want to say electron.. 😅
Sir, quantum mechanics ke kya kya topics aane chahiye for learning Quantum Computing?
Whole quantum mechanics.
Waise to jitna seekho utna acha hai, but density matrix tak to sab ache se karlo.
Bhai I wanna join sciastra next year as I am in 10th now and want to become both physicist and biologist love them.
But I lack mathematics skills how can I improve like how to solve and think logically?
Abhi thoda life ke maje karo...
@@SciAstrahan but I love it so abhi to bohot cover karna he physics me aur tabhi to aage ki research kar paunga Jo aur koi nhi kiya he😍
@@bhaktabachalabehera2654abhi se 11th , 12th ka padhne ki jarurat nahi hai chill karo masti, badmashi, pagal pan school jane wale bache ko suit karegi scientist ko nahi isliye 😄
How is Rasenick halliday international version
Which version?
@@Ssj-mj4ic international one
@@Prakhar.56 excellent
Sir you are now in odisha I am also from odisha ❤❤ and maths is my fav sub.🩵♾️
Nice, kabhi milte hain :)
@@SciAstra thanks bhaya
😊
Share it if you liked it :)
As a class 12th student, except KIT KAT sab kuch samajh aya 😂😂😂 bc'z I love Mathematics ❤
🙂
Finally.....
Quatum mechanics agya
Abhi aur aa raha hai :)
@@SciAstra bhiya pahali bar kisina physics bohot fun sa sikhya ..(*❛‿❛)→
abhi toh start bhi nahi hua
Yeh!! I am first here
🎉