Free Particle in Quantum Mechanics

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In quantum mechanics, the wave function of a free particle is often described using plane wave solutions. These plane waves represent particles with definite momentum and energy, but they come with certain issues:
Non-Normalizability: Plane waves extend infinitely, meaning their total probability density cannot be normalized to one. This conflicts with the probabilistic interpretation of the wave function.
Lack of Localization: A plane wave implies the particle is spread out over all space, making it impossible to determine its exact position.
To address these issues, the concept of a wave packet is introduced. A wave packet is a combination of multiple plane waves with different momenta. This superposition of waves results in a localized wave function, allowing the particle to be confined to a specific region in space.
Wave packets provide a more accurate representation of free particles in quantum mechanics. They allow for a localized position, which aligns with the probabilistic nature of quantum mechanics, and they can spread over time, reflecting the inherent uncertainty in a particle's momentum and position.
00:00 Introduction
01:19 Schrodinger's Equation - Solution
09:25 Constant Probability Density of Plane waves
12:39 Velocity of Plane waves
15:01 Non-Normalizability of Plane waves
17:24 Concept of Wave Packet
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[@adityanastik8098]

I am PG qualified in political science and international relations.....
Please.. continue sir.... due to financial problems I didn't study science but I am much more interested in Quantum mechanics....😢😢😢

[@victorporras5560]

Wonderful, thanks

[@waybeyond1176]

it was really a great explaination for free particle!!

[@SergeyPopach]

Can you, please, explain the time evolution of a free particle at which the spread of Gaussian distribution increases at t>0? Why the continuous bandwidth of a linear combination of frequencies (p=hk) would expand over time (dispersion effect)? What this physically means for a particle such as electron or light waves?

[@SergeyPopach]

Great explanation!

[@user-nf2mg5oh2h]

wonderful lecture...

[@ramasubbu2890]

Wonderful lecture sir

[@satyampanchal-1016]

Hi, Sir, I was actually doing something advanced and calculating the free particle kernel via path integral. The probability density I get from that Is SAME as what I got when I calculated it for a particle under a constant force..Can you comment on why the case of a free particle and a particle under a constant force is the same as far as position space probability density is concerned?

[@abandz1132]

If the plane wave solution is treating the particle like a wave then shouldn’t it be normal for it to get a different velocity than the particles.

[@fehmi35]

Please make a video on Schrödinger equation periodic potential solution, bloch function, electron bands etc.

[@pauldirac6243]

Dibs is cool

[@mathvanshi7921]

Please make lecture series on general theory of relativity

[@Bitastro]

👍👍👍

[@rahulkumar-zm6rz]

❤❤❤❤🙏🙏🙏🙏🙏🙏

[@ANKITKUMAR-yp6hq]

Sir Hindi me bhi upload kariye plzzz..... हम आपके द्वारा दिए गए ज्ञान के प्यासे हैं,🙏

[@FortheLoveofPhysics]

Hi Ankit, I appreciate your request. Since I already started this QM series in English, I think it's best I finish it similarly. In future I might do a lecture series on Hindi, if there's enough students who would prefer that

[@MichaelKingsfordGray]

How can a "free" particle be travelling?
Relative to what? The observer?
If it is relative to ANYTHING, then it is NOT free!

[@FortheLoveofPhysics]

In Physics, object's motion is always studied wrt a frame of reference. That has nothing to do with being "free" which simply means it's not experiencing any external force

[@radheshyamsingh3604]

Sir in hindi

[@pauldirac6243]

First😊

[@hare_krishna716]

Wonderful lecture sir