Wave Function in Momentum Space

What is the representation of Wave function in Momentum space, and the corresponding probability densities and expectation values?

𓏬𓏬𓏬𓏬𓏬ELEVATE CLASSES𓏬𓏬𓏬𓏬𓏬
Upcoming Batch: Physics IIT-JAM 2025, TIFR & JEST Batch starting JUNE 22
Upcoming Batch: CSIR-NET DEC 2024 & GATE-2025 Batch starting JUNE 30

Find all details here:

𓏬𓏬𓏬𓏬𓏬LEC NOTES - GDRIVE𓏬𓏬𓏬𓏬𓏬
Find the PDF Scanned copy of my NOTES for this lecture here:

𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬
In quantum mechanics, the wavefunction can be represented in both position space and momentum space. The wavefunction in position space describes the probability amplitude of finding a particle at a specific location. In momentum space, the wavefunction describes the probability amplitude of a particle having a specific momentum.

This momentum space representation is obtained through a mathematical transformation, allowing physicists to analyze and understand phenomena where momentum, rather than position, is the key variable. This is particularly useful in problems involving conservation of momentum, scattering, and analyzing particle dynamics in various potential fields.

By examining the wavefunction in momentum space, we gain insights into the particle's behavior and properties related to its momentum, providing a complementary perspective to its position space representation.

00:00 Introduction
03:20 Fourier Transform
14:48 Momentum Space Representation
31:03 Problem Solving

𓏬𓏬𓏬𓏬𓏬𓏬TELEGRAM𓏬𓏬𓏬𓏬𓏬𓏬

𓏬𓏬𓏬𓏬𓏬SUPPORT CHANNEL𓏬𓏬𓏬𓏬𓏬
Your Financial support provides me an additional incentive to create high quality lecture videos. I am very much thankful for your generosity and kindness

JOIN MEMBERSHIP in Youtube 😇😇😇

[FortheLoveofPhysics]

Upcoming Batches:

Physics IIT-JAM 2025, TIFR & JEST Batch starting JUNE 22
CSIR-NET DEC 2024 & GATE-2025 Batch starting JUNE 30

[ajittiwari]

Please continue adding lectures on Quantum Mechanics ❤
Such a brilliant teacher

[nadjetbf]

Sir please we need atomic courses if you can .
Thank you so much for your help in previous subjects

[mazharali]

Thank you so much sir for continuing this lect series❤

[itsawonderfullife]

Thanks for the video. Is that the fact that instead of a Dirac delta (centered at k0) as the Fourier transform (momentum space wave function) you obtained a sinusoidal function of p, an artifact of limits of integration? I mean "a" instead of infinity? Because Fourier transform of a pure frequency signal (in x or t space) should be delta function centered at that frequency (in p or f space), if I understand correctly.

[Astrophysics]

Sir I'm for very grateful to you for these type of crystal clear conceptual lectures, but sir please make one video/ week atleast 🙏🙏

[SergeyPopach]

very straightforward, but shallow lecture… no depth provided for insight at all.. without understanding functional orthogonality, projection of wave function upon orthonormal basis, inner product and all other key properties of Hilbert space this material remains for students, viewers undiscovered mystery that just needs to be memorized, copied and pasted…