Proof: Electron Probability is Independent of φ #mscphysics #crazyphysics #shorts #handwrittennotes

In this video, we prove that the probability of finding an electron in a hydrogen-like atom is independent of the angle φ (phi). This is a very important concept in Quantum Mechanics (BSc & MSc level) and is frequently asked in exams.

We start from the hydrogen atom wavefunction and use spherical harmonics to show that although the wavefunction contains e
imφ
, it disappears when we take modulus square. Hence, the probability density becomes independent of φ.

📌 Topics Covered:
✔ Hydrogen-like atom wavefunction
✔ Spherical harmonics
✔ Probability density ∣ψ∣
2

✔ Role of e
imφ

✔ Step-by-step derivation

👉 This video is helpful for:

BSc Physics students
MSc Physics students
Quantum Mechanics learners
Exam preparation (University exams)

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Видео Proof: Electron Probability is Independent of φ #mscphysics #crazyphysics #shorts #handwrittennotes канала Crazy Physics