I Different expressions about time reversal and confusion

hokhani
Messages
552
Reaction score
15
TL;DR Summary
Discrepancy between Sakurai and Bruus
In Sakurai, section 4.4, says that if ##\psi(x,t)## is a solution of Schrodinger equation then ##\psi^*(x,-t)## is always another solution. However, in the corrected version of "Many-body Quantum Theory in Condensed Matter Physics, Bruus and Flensberg, 2016", section 7.1.4, restricts this condition and says that if we have time reversal symmetry ##H=H^*## then ##\psi^*(x,-t)## would be another solution. I would like to know which of these statements is correct.
 
Last edited by a moderator:
Physics news on Phys.org
hokhani said:
TL;DR Summary: Discrepancy between Sakurai and Bruus

In Sakurai, section 4.4, says that if ##\psi(x,t)## is a solution of Schrodinger equation then ##\psi^*(x,-t)## is always another solution. However, in the corrected version of "
Many-body Quantum Theory in Condensed Matter Physics, Bruus and Flensberg, 2016", section 7.1.4, restricts this condition and says that if we have time reversal symmetry ##H=H^*## then ##\psi^*(x,-t)## would be another solution. I would like to know which of these statements is correct.
Sakurai must assume that the Hamiltonian has that property in general. It's not hard too see from the SDE that ##H = H^*## is required for this to make sense.
 
Last edited:
  • Like
Likes Albertus Magnus
Thanks, it seems that for the Hamiltonian in Sakurai, ##H=\frac{P^2}{2m}+V(x)##, which is in the position space, the Hermitian condition ##H=H^{\dagger}## fulfils automatically ##H=H^*## since ##V^\dagger=V## demands ##V=V^*##.
 
  • Like
Likes Albertus Magnus, Demystifier and PeroK
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!

Similar threads

Replies
8
Views
790
Replies
9
Views
2K
Replies
21
Views
3K
Replies
1
Views
1K
Replies
19
Views
2K
Replies
3
Views
2K
Back
Top