Degeneracy in QM

What is Degeneracy in Quantum Mechanics? I explain it using the example of Particle in a 3D Box.
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• Quantum Mechanics
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QM LEC 35
In quantum mechanics, degeneracy refers to the situation where two or more distinct quantum states share the same energy level. These states are said to be degenerate. Degeneracy typically arises due to symmetries in the system, where the system’s Hamiltonian (which describes its energy) has certain symmetries that lead to multiple states having the same energy.
Degeneracy plays a crucial role in various quantum systems, influencing how systems respond to perturbations and how they behave in fields such as statistical mechanics and quantum computing.
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[@FortheLoveofPhysics]

Complete Introduction to QM Playlist: kzbin.info/aero/PLRN3HroZGu2mCtdalEmZAM2nr1xBWAtUn

[@samuelmr677]

Very exact timing sir, I was trying to understand the same topic and you made the lecture .😅

[@FortheLoveofPhysics]

Glad to hear that :)

[@KnockVoid]

Glad to hear that :)

[@oreasunchez5438]

im study physics in South Korea and your videos are soooooooo helpful , thanks you very much!!!

[@KnockVoid]

Glad to hear that :)

[@laymanphysicist964]

Sir, why is there only 2 2 2 combination in the fifth excited state?

[@roshan0405]

Your hair is giving me extra vibe in this video,love it❤

[@chudleyflusher7132]

👍😂

[@divyakumar8147]

Thanks sir this playlist has been quite insightful and amazingly full of mind blowing concepts whose satisfactory and deep explanation were given, I can say in full confidence that you have done justice to channel name for the love of physics, now I love you along with physics as well, hope to see such interesting content from you in the future as well.

[@JaydeepMakwana-l3t]

Great Lecture as always❤

[@lovephysicstoo]

Professor Das, great lecture. Learned a lot from you. I understand for 3D particle in box, we have 3 quantum numbers, nx, ny and nz in each direction. In one of the last slides on the hydrogen atom, you showed up to 7 quantum numbers. For n=3, there are 9 configurations. Do these 9 configurations (1s, 3p, 5d) map to to the 5 excited states (ground, first, second, third, fourth) that you talked about in the entire lecture? Basically, I would like to know how your entire talk in this lecture map to the slide on H atom. Thx for your help.

[@lovephysicstoo]

As an example, we have 𝛙122, 𝛙311, 𝛙111, 𝛙222 and on and on, how does it map to that hydrogen atom slide that you showed briefly in the video? Hope I am clear.

[@FortheLoveofPhysics]

Hi, many qm systems have multiple quantum numbers, that decide the energy of the state. For eg, in 3D infinite potential well a state is characterized by (nx,ny,nz) and for a symmetric well (all sides equal), 𝛙122, 𝛙221, 𝛙212 will share the same energy level. (This is determined by the Energy formula). Hence these states are degenerate, even though their wavefunctions (and corresponding probability densities are uniquely different). Now, coming to the H-Atom, the quantum numbers are different - (n,l,m,s) that can all take different values (there are some rules). But the Energy of a state in H-Atom is purely decided by "n" (also known as the principal quantum number), and other numbers don't have a role, as E=-13.6/n^2 Hence in H-atom, in the chart for n=3, there are 9 possible unique wavefunctions (and their corresponding probability densities, known as orbitals) but all of them share the same energy level. So n=3 is 9-fold degenerate. Hope this helps

[@lovephysicstoo]

@@FortheLoveofPhysics Excellent sir. I got it. Thx for your explanation. From a higher scope, I've listened to more than half dozen your lectures (Schrondinger's equation, stationary state, free particle, particle in a box, ket-bra ...) and in the meantime, I have also been following other introductory lectures on quantum computing elsewhere (concept of superposition, measurement, entanglement, rotation and Bloch sphere etc.), I would like to know qualitatively if and how these unique wavefunctions with same energy level would relate to the number of qubits in quantum computing. I have a feeling that they are strongly connected but have not reached that "ah-ha" moment. If there is a need to take more than a few sentences to explain things, I would love to see a lecture on how quantum mechanics that you've taught (40+ lectures) would tie directly to quantum computing and in particular, the count of qubits. Just looking for some qualitative insight here if you understand what I mean. Thx for your prompt reply. Love this site.

[@ummulbnaeen3]

thank u sir......your videos are always helpfull in undersatanding concept of physics ........sir please do upload a vedio on 3D harmonic oscillator......

[@dr.maheshkumar3692]

Nice explained with best examples. Thanks

[@muhammadrashidmuhammadrash2585]

Great lecture sir ❤

[@benmenanaazdine2782]

Thank you very much sir. can you do a lecture about giant resonance in nuclei

[@sword0825]

how we can go from state to another state , what is the pattern we need to take to go for example from the second exited state to third exited state and thanks for the video

[@FortheLoveofPhysics]

Second and Third excited states are orthogonal states. Hence they won't evolve from one to the other, on their own (time evolution). They only way that can happen is if the system is subjected to an external perturbation (like the presence of a external photon of appropriate frequency)

[@sword0825]

@@FortheLoveofPhysics first thanks for the clarification , so in the video you assumed that there is a external perturbation on every jump from state to state

[@amartyatats7125]

love this

[@ravishankaryadav9473]

Nice explanation

[@RanaAli-tc4eu]

Love from Lahore❤Pakistan🇵🇰

[@soumyatanuganguly9656]

Sir please provide some videos on covariant formulation of electrodynamics or please tell some reference from where I can learn this topic.....please sir

[@Vaishnav_96643]

Thanks sir

[@pankaj.706]

Great lecture but making more vedios numerical on quantum mechanics tifr asked questions

[@agustineguiguren1445]

Why are all n equal to 1 and not 0 in the ground state?

[@FortheLoveofPhysics]

0 would lead to a vanishing wave function, which is not possible

[@elsa-g6h]

sir can you please do a video related to energy levels in 2d box

[@FortheLoveofPhysics]

2D box energy levels is very similar to the 3D box. U just substitute (nx,ny) with (1,1), (2,1)&(1,2), (2,2) and so on

[@srimirasrimira9291]

Waiting for your perturbation concepts sir

[@DanielMichel-r1w]

👏👏

[@aftabsayed2825]

Sir your lectures are boring, 😑

[@FortheLoveofPhysics]

How do u think can it be improved?

[@ravishankaryadav9473]

Kya baat krte ho bhai 😮 it's best lecture for understanding concept

[@NUMANKHAN-kn1hv]

@@FortheLoveofPhysics Sir please make you lectues in Hindi.

[@JaydeepMakwana-l3t]

achha mazak tha

[@agnelomascarenhas8990]

​@@FortheLoveofPhysics The lecture content is superb, clear. I have no formal physics background, but I enjoy the mathematical models. Blackboard is difficult to read clearly due to handwriting and contrast. Slides maybe better or perhaps other methods. Thank you for the quality work!