Quantum Exam Review: Answers & Info to Questions

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SUMMARY

The forum discussion focuses on preparing for a quantum mechanics exam, specifically addressing key concepts such as the Time Dependent Schrödinger Equation (TDSE) and Time Independent Schrödinger Equation (TISE). Participants emphasize the importance of understanding stationary states, states of definite energy, and the use of operators like H, p, and x. They recommend consulting authoritative texts, such as Cohen-Tannoudji's, for comprehensive explanations and solutions to the posed questions. The discussion underscores the necessity of engaging with lecture notes and textbooks rather than seeking direct answers.

PREREQUISITES
  • Understanding of the Time Dependent Schrödinger Equation (TDSE)
  • Familiarity with the Time Independent Schrödinger Equation (TISE)
  • Knowledge of quantum operators, specifically H (Hamiltonian), p (momentum), and x (position)
  • Ability to calculate expectation values in quantum mechanics
NEXT STEPS
  • Study the derivation and applications of the Time Dependent Schrödinger Equation (TDSE)
  • Explore the concept of stationary states and their significance in quantum mechanics
  • Learn how to calculate expectation values using quantum operators
  • Read Cohen-Tannoudji's textbook on quantum mechanics for foundational concepts
USEFUL FOR

Students preparing for quantum mechanics exams, educators teaching quantum physics, and anyone seeking to deepen their understanding of quantum mechanics principles and equations.

NepToon
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These are not homework questions. Review for the test rather; I was wondering if I could get answers or links to any info regarding this set of questions. Thanks in advance.

1) What equation governs the regular time evolution of the wave function? Are there other ways a wave function can evolve (change with time)?
2) What is meant by a "stationary state"?
3) What equation, when solved, gives stationary states for a given potential?
4) What is meant by a state of definite energy? How are stationary states and states of definite energy related?
5) How do you write down the general solution to the TDSE (Time Dependent SE) given the solutions to the TISE (Time Independent SE)?
6) Make sure you know how to use your operators, H, p and x. (These should have hats on them but email will not allow this!)
7) Make sure you know how to calculate expectation values, etc.
 
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Getting direct answers as you probably want/like is not really in your benefit. These forums or the lecture notes won't be there in the exam with you. My advice is to track down the notions in each of the 5 questions in your notes. (Presumably correct) answers to these questions must be there. Or if the notes are wrong/incomplete, then a book like Cohen-Tannoudji's et al.'s should more than compensate.
 
I don't really know what answer you'd be looking for other than "Learn Basic Quantum Mechanics". Grab a quantum book, read the first chapter.
 
We treat all textbook-style questions as homework, even when they're not. So you're going to have to post your attempts to solve these problems before we can help you.

If you have no idea where to begin with one of these problems, it's OK to say that, and we'll help you get started.
 
Steger said:
[...] Grab a quantum book, read the first chapter.

That depends on the book, of course. Reading the first chapter in most books will get him acquainted with blackbody radiation, which is not what he needs.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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