Quantum Physics - Hamiltonian operator

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SUMMARY

The discussion centers on the Hamiltonian operator in quantum physics, specifically addressing how to demonstrate that a certain quantity remains constant over time. Participants emphasize the importance of starting with a clear expression for the quantity in question, followed by taking its time derivative to analyze its behavior. The Hamiltonian operator plays a crucial role in this process, as it governs the evolution of quantum states. The conclusion drawn is that a thorough understanding of the time derivative and the Hamiltonian is essential for solving such problems.

PREREQUISITES
  • Understanding of the Hamiltonian operator in quantum mechanics
  • Familiarity with time derivatives in calculus
  • Basic knowledge of quantum state evolution
  • Concept of conservation laws in physics
NEXT STEPS
  • Study the mathematical formulation of the Hamiltonian operator in quantum mechanics
  • Learn how to compute time derivatives of quantum observables
  • Explore the implications of conservation laws in quantum systems
  • Investigate examples of time-independent quantities in quantum mechanics
USEFUL FOR

Students of quantum physics, researchers in theoretical physics, and anyone interested in the mathematical foundations of quantum mechanics.

Mankul
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Hi, Can you help me with this, I don't know how to go about solving this.

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You have to show "something" does not change with time. So, start with writing down an expression for that "something", then take the time derivative, and see how far you get.
 

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