Quantum Mechanics is NOT what you think 😢 | Lecture 06

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#quantum #quantumphysics #physics

Опубликовано:

10 сен 2024

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Комментарии : 22

@SciAstra Месяц назад

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@furiousbro4685 3 дня назад

make a video on action principle

@Iam_Batman. 23 дня назад

Thank Sagar bhaiya and sciAstra. Its a great series. ❤❤❤

@Iam_Batman. 23 дня назад

Its a great series, easy and a bit confusing. ❤️‍🔥❤️‍🔥

@user-ee2xw5xq1f 25 дней назад

yes bhaiya please action principle par video zarur bnana and thank you so much for this amazing series 😄🥰🥰

@Krishnanjan_Sil Месяц назад

Amazing series for beginners 👍🏻

@SciAstra Месяц назад

Glad to hear that!

@shashvitaratra Месяц назад

### Real-Life Analogy: Think about having two sets of items: - Set 1: apples and oranges - Set 2: red and green If you combine every item from the first set with every item from the second set, you get: - Red apple - Green apple - Red orange - Green orange This combination of items is similar to what happens in a tensor product. ### Tensor Product in Simple Terms: 1. **Combining Spaces**: - Imagine you have two groups of vectors (think of vectors as arrows pointing in different directions). - The tensor product combines these groups to create a new, larger group that includes all possible pairs of arrows from the original groups. 2. **Constructing the New Space**: - If you start with two vectors from each group, say one pointing north and another pointing east, you combine them in every possible way to form new vectors in the combined space. - The new space will be bigger and include all the combinations of the original vectors. 3. **Properties**: - The combination is linear, meaning you can add and scale the vectors in the new space similarly to how you did in the original spaces. ### Example in Quantum Mechanics: Imagine you have two quantum particles: - One particle can be in a state where it is either up or down. - Another particle can be in a state where it is either left or right. To describe the combined system of both particles, you use the tensor product: - The combined states would include all possible combinations: - Up and left - Up and right - Down and left - Down and right ### Key Points to Remember: - The tensor product is a way to combine two sets of vectors (or states) into a new, larger set that includes all possible combinations. - This new set contains pairs of vectors from the original sets. - In quantum mechanics, it helps describe the state of combined systems. In essence, the tensor product is like creating a new group by pairing each item from one group with each item from another, giving you a comprehensive way to describe combined systems.

@Krishnanjan_Sil Месяц назад

Penrose got Nobel prize with the A.K. Raychaudhuri's equation.

@SciAstra Месяц назад

❤️

@aigamer79 Месяц назад

want action principle videooo!!!!!! bhaiya

@Iam_Batman. 23 дня назад

Bhaiya pls Action pricipal per ek lecture as a ending series video. And thanks a lot .

@shashvitaratra Месяц назад

In quantum mechanics, observables are physical quantities that can be measured, such as position, momentum, and energy. Here's a simple way to understand them: ### Real-Life Analogy: Imagine you have a dice. When you roll it, the number that lands face up is a measurable outcome. In this analogy: - The **dice** represents a quantum system. - The **number** on the face of the dice represents an observable (something you can measure). ### Quantum Observables: 1. **What are they?** - Quantum observables are properties of a quantum system that you can measure. Examples include: - **Position**: Where is the particle? - **Momentum**: How fast and in which direction is the particle moving? - **Energy**: How much energy does the particle have? 2. **How do we describe them?** - In quantum mechanics, observables are represented by mathematical objects called **operators**. - An operator acts on the wave function (which describes the quantum state) to give information about the observable. 3. **Measurement and Probabilities:** - Unlike classical physics, measuring a quantum observable doesn’t always give the same result. Instead, it gives a range of possible outcomes, each with a certain probability. - For example, if you measure the position of an electron, you might get different positions each time you measure, according to a probability distribution. ### Example: Measuring Position Imagine trying to find an electron in a box: - **Before Measurement**: The electron is described by a wave function, which gives the probability of finding the electron at various positions. - **Measurement**: When you measure the position, you get a specific result, like finding the electron at a particular spot in the box. - **After Measurement**: The wave function collapses to reflect the new information you have about the electron's position. ### Key Points to Remember: - Quantum observables are the properties of a system that can be measured. - Measurements in quantum mechanics give probabilities of different outcomes, not certainties. - Observables are described by operators that act on the system's wave function. In essence, quantum observables are a way to connect the abstract mathematical description of a quantum system to real-world measurements and experiments.

@shashvitaratra Месяц назад

Imagine you have a cup of hot coffee. Right after it's poured, the coffee is very hot. However, as time passes, the coffee gradually cools down. This cooling process is an example of time evolution. In this case, the system is the cup of coffee, and its state is defined by its temperature. The change in temperature over time (cooling down) is the time evolution of this system. Here’s a step-by-step breakdown: 1. **Initial State**: The coffee starts at a high temperature. 2. **Time Progresses**: As time goes on, the coffee loses heat to the surrounding air. 3. **New State**: After some time, the coffee's temperature decreases. We can describe this process mathematically using Newton's Law of Cooling, which states that the rate at which the coffee cools is proportional to the difference between its temperature and the ambient temperature. This law provides a formula to predict the temperature of the coffee at any given time. So, in simple terms, time evolution is just how things change with time. In the coffee example, it's how the temperature changes as time passes.

@DeepakKumar-rb3sq Месяц назад

bhaiya make a vidio on particles physics

@SciAstra Месяц назад

Done :)

@gautamchoubey1275 Месяц назад

Please bhaiya dont stop 🛑 series we are getting intrest in it

@SciAstra Месяц назад

Ab jald hi naya series aayega

@Krishnanjan_Sil Месяц назад

Sir, can you please make videos on how symmetries are exploited in Physics like Noether's theorem and so on.

@Chaitanya-iiserpune Месяц назад

Bhaiya make the series of least action principle ... Will love the vedio🥰

@samiddhajana01 Месяц назад

❤❤

@shashvitaratra Месяц назад

Zeno's paradoxes are a set of philosophical problems that were introduced by the ancient Greek philosopher Zeno of Elea to challenge our understanding of motion and change. One of the most famous of these paradoxes is "Achilles and the Tortoise." **Achilles and the Tortoise Paradox:** 1. **The Setup**: Imagine a race between the swift Achilles and a slow-moving tortoise. To make the race interesting, the tortoise is given a head start. 2. **Zeno's Argument**: - Achilles runs much faster than the tortoise, but according to Zeno, he will never be able to overtake it. - When Achilles reaches the point where the tortoise started, the tortoise has moved a bit further ahead. - When Achilles reaches that new point, the tortoise has moved further again. - This process continues indefinitely, with Achilles always having to reach a new point where the tortoise has just been, and the tortoise always moving a little further ahead. **The Paradox**: It seems to imply that Achilles can never catch up with the tortoise, even though we know from experience and logic that he will eventually overtake the tortoise. **Modern Resolution**: The paradox arises from a misunderstanding of the concepts of infinity and convergence. In modern mathematics, particularly calculus, we understand that: - The distances Achilles must cover get smaller and smaller. - The sum of an infinite series of decreasing distances can converge to a finite limit. So, while Achilles has an infinite number of points to reach (where the tortoise has been), the total time it takes him to catch the tortoise is finite. Therefore, Achilles will indeed overtake the tortoise after a certain amount of time, resolving the paradox. In essence, Zeno's paradoxes highlight the counterintuitive nature of infinity and motion, prompting deeper exploration and understanding in mathematics and philosophy.