Hellow guys, Welcome to my website, and you are watching The quantum virial theorem. and this vIdeo is uploaded by Professor M does Science at 2022-06-30T04:00:24-07:00. We are pramote this video only for entertainment and educational perpose only. So, I hop you like our website.
| Name | The quantum virial theorem |
| Video Uploader | Video From Professor M does Science |
| Upload Date | This Video Uploaded At 30-06-2022 11:00:24 |
| Video Discription | 💻 Book a 1:1 session: https://docs.google.com/forms/d/e/1FAIpQLScUL187erItvC7GPnNU2pelsueyVFr94nRq2A5Eq2aVRdGiIQ/viewform?pli=1 📚 Evaluating expectation values in quantum mechanics typically requires lengthy maths. For example, if we work in the position representation in terms of wave functions, evaluating expectation values typically requires evaluating lengthy integrals. In this video we derive the virial theorem, which provides a very simple relation between the expectation value of the kinetic and potential energies of any quantum system. Such a relation allows us to bypass the lengthy evaluation of expectation values and learn about our system in a simple and transparent manner. We also discuss the special case of potentials described by homogeneous functions, in which the virial theorem takes an even simpler form. Examples we discuss include the quantum harmonic oscillator, the hydrogen atom, and also molecular systems and materials made of many atoms. 0:00 Intro 0:37 Hypervirial theorem 2:57 Virial theorem for 1 particle in 1D 9:13 Virial theorem for potentials described by homogeneous functions 15:25 Virial theorem for multiple particles in 3D 22:29 Wrap-up ⏮️ BACKGROUND Eigenvalues and eigenstates: https://youtu.be/p1zg-c1nvwQ Hermitian operators: https://youtu.be/XIgDUfyrLAY Expectation values: https://youtu.be/rEm-Ejg5xek Commutator algebra: https://youtu.be/57xgSIV9PY0 Functions of operators: https://youtu.be/nqLEbrzVsk4 Quantum harmonic oscillator playlist: https://www.youtube.com/playlist?list=PL8W2boV7eVfmdWs3CsaGfoITHURXvHOGm Hydrogen atom playlist: https://www.youtube.com/playlist?list=PL8W2boV7eVfnJbLf-p3-_7d51tskA0-Sa ⏭️ WHAT NEXT? Hydrogen atom ground state: [COMING SOON] ~ Director and writer: BM Producer and designer: MC |
| Category | Education |
| Tags | quantum | quantum mechanics | Cavendish Laboratory | University of Cambridge | Cambridge University | mathematics | Euler's theorem | Euler theorem | homogenous functions | homogeneous function | virial theorem | hypervirial theorem | expectation value |
