What is meant by "basic" quantum mechanics?

[Wrichik Basu]

I have been taking many online courses. In the prerequisites for many courses, it has been mentioned, "basic" quantum mechanics.

It has become important to define where the boundary of basic ends and the advanced level starts, though I believe that is not well defined. I have been studying QM since some time, and hence I want to know what are the basics of QM.

I have a list of topics. Please tell me if anything should be added or excluded.

1. The concept of wave function and probability
2. Uncertainty Principle
3. Operator algebra and operator formulation rules (eigenstates, eigenvalues, types of operators and how to use them)
4. Schrödinger Equation
5. Probability Current density
6. Infinite Square Well
7. Finite Square Well
8. Attractive Delta Function
9. Linear Harmonic Oscillator
10. The Step Potential
11. Angular Momentum
12. Spin Angular Momentum
13. Central potential problems in 3D
14. Maxwell-Boltzmann statistics
15. Bose-Einstein Statistics
16. Fermi-Dirac Statistics

Wherever applicable, the topics include finding the eigenvalues and eigenfunctions.

 

[Dr. Courtney]

For me, "basic quantum mechanics" always includes the hydrogen atom.

 

[Wrichik Basu]

For me, "basic quantum mechanics" always includes the hydrogen atom.

Somehow forgot to add that.

 

[Dishsoap]

To me, "basic" quantum mechanics includes the topics covered in Griffiths' QM book. It looks like you've summed up the topics covered quite nicely.

 

[Dr. Courtney]

Just remembered this one, thanks to a Physics major asking me some questions.

https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics)

 

[Wrichik Basu]

To me, "basic" quantum mechanics includes the topics covered in Griffiths' QM book. It looks like you've summed up the topics covered quite nicely.

But I've not taken them from Griffiths' book.

 

[jtbell]

I have been taking many online courses. In the prerequisites for many courses, it has been mentioned, "basic" quantum mechanics.

To me, "basic quantum mechanics" means the stuff covered in a typical "introductory modern physics" course which in the US comes after a first-year course using something like Halliday/Resnick or Young/Freedman, and before a full-on QM course using something like Griffiths. For many years I taught such a course, and still have a copy of Beiser's Concepts of Modern Physics (6th ed., 2003).

• Chapter 5: Quantum Mechanics
  • The Wave Equation
  • Schrödinger's Equation: Time Dependent Form
  • Linearity and Superposition
  • Expectation Values
  • Operators, eigenfunctions and eigenvalues
    
  • Schrödinger's Equation: Steady-State Form (a.k.a. time independent S.E.)
  • Particle in a Box
  • Finite Potential Well
  • Tunnel Effect
  • Harmonic Oscillator
• Chapter 6: Hydrogen Atom
  • Schrödinger's Equation in spherical coordinates
  • Separation of Variables
  • Quantum numbers: principal, orbital, magnetic
  • Probability densities
  • Transitions and selection rules
  • Zeeman effect

No Dirac notation. Orthogonality of eigenfunctions was discussed only in an exercise. (However, the intro modern course that I took as an undergraduate did discuss orthogonality and orthonormality, and extracting the coefficients of an eigenfunction expansion.) In the hydrogen atom, we did not derive the Legendre polynomials for the angular part of the solution, but simply presented them as the solutions. For the radial part, we simply presented the energy eigenvalues (no discussion of Laguerre polynomials).

 

[nrqed]

I have been taking many online courses. In the prerequisites for many courses, it has been mentioned, "basic" quantum mechanics.

It has become important to define where the boundary of basic ends and the advanced level starts, though I believe that is not well defined. I have been studying QM since some time, and hence I want to know what are the basics of QM.

I have a list of topics. Please tell me if anything should be added or excluded.

1. The concept of wave function and probability
2. Uncertainty Principle
3. Operator algebra and operator formulation rules (eigenstates, eigenvalues, types of operators and how to use them)
4. Schrödinger Equation
5. Probability Current density
6. Infinite Square Well
7. Finite Square Well
8. Attractive Delta Function
9. Linear Harmonic Oscillator
10. The Step Potential
11. Angular Momentum
12. Spin Angular Momentum
13. Central potential problems in 3D
14. Maxwell-Boltzmann statistics
15. Bose-Einstein Statistics
16. Fermi-Dirac Statistics

Wherever applicable, the topics include finding the eigenvalues and eigenfunctions.

What is ``linear" harmonic oscillator?

For me, basic QM includes some perturbation theory, at least time independent. But many could disagree.

 

[Klystron]

What is ``linear" harmonic oscillator?...

I have encountered the term "linear" harmonic oscillator in pre-1970's electronic design documents describing parametric amplifiers in the microwave spectrum.

Though seemingly contradictory terms I rationalized them at the time to refer to altering (apparently) linear parameters to change the resonant frequency of the oscillator. Simple example utilizing microwave (cm) waveguide: alter the cavity dimension by sliding an adjustable segment along the x-axis. A small "linear" displacement results in significant harmonic relocation. Hence, linear harmonic oscillator (LHO). [Note: this was a working hypotheses, unproven.]

After learning more mathematics I further rationalized the term "linear" to refer to first order solutions of ordinary differential equations that describe harmonic oscillation. While learning Min-Max applications in a linear algebra course, the instructor included a simple LHO circuit in a quiz. [Any confusion at this point is due to my poor skills describing math, not to mention using examples from electronics.]

Back to "Basic QM": If the OP assigns priority to the elements in their list, suggest they move #4 Shrodinger equations to just after, or combined with, #1 wave function.

Suggest prioritizing your study of #11 Angular momentum and #12 "spin momentum" and/or adding list element "Spin". I'm currently reading Roger Penrose "Road to Reality" again who regularly uses spin and spinors to inform the reader's understanding of the nature of reality at a quantum level.
( Penrose and Hawking wrote several helpful highly readable essays describing spacetime.)

List element #2: While Math is the "language of physics", many influential physicists thought, wrote, and spoke German. The German term "uncertainty" does not translate directly into English. Many myths and misunderstandings arise from overly broad translations of German into English in popular literature.

 

[Wrichik Basu]

What is ``linear" harmonic oscillator?

I am talking of the simplest case of an oscillator with potential $\frac{1}{2} m \omega ^2 x^2$. That's why linear.

 

[Wrichik Basu]

Back to "Basic QM": If the OP assigns priority to the elements in their list, suggest they move #4 Shrodinger equations to just after, or combined with, #1 wave function.

Suggest prioritizing your study of #11 Angular momentum and #12 "spin momentum" and/or adding list element "Spin". I'm currently reading Roger Penrose "Road to Reality" again who regularly uses spin and spinors to inform the reader's understanding of the nature of reality at a quantum level.
( Penrose and Hawking wrote several helpful highly readable essays describing spacetime.)

The list is not a priority list. So the topics may be in any order. Anybody who decides to study using this list, should use a good book which has most of these topics. The author shall take care of priority.