Faculty Disagreement about the Teaching of Quantum Mechanics

Michael Dubson+, Steve Goldhaber+, Steven Pollock+, and Katherine Perkins*+

+Physics Dept and *Science Education Initiative U. of Colorado at Boulder

Interviewed 27 faculty who teach QM 22 from CU 5 from other schools

Examined 20 junior-level QM textbooks.

Our Department is engaged in a major transformation of junior-level E&M and QM courses, making them more interactive with

• Clicker questions/peer instruction• White-board activities• Group-work tutorials

In discussions with our faculty, we find consensus on content of E&M, but a wide variety of opinions about content and pedagogy of QM. To gauge range of opinions among faculty about teaching of QM, we developed a survey, and

Introduction

In the past...no dominant undergrad QM text.

Textbooks used by faculty when they were undergrads:

No text (4)Gasiorowicz (5)Saxon (3)Schiff (3)Eisberg&Resnick (2)Anderson (2)French&Taylor (2)Morrison (1)Shankar (1)Rae (1)Dicke&Wittke (1)Dirac (1)

Today, Griffiths dominates the market44 of 68 other schools polled (65%) currently us Griffiths.

17 out of 27 faculty (63%) polled use, or will use, Griffiths.

$109 on Amazon

"It would be a catastrophe if everyone used my book. " –David J. Griffiths

What Text Do You Use?

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Griffiths Other text No text Undecided

Faculty preference: Postulates or Not?Q for faculty: A few textbooks clearly state the "Postulates" of QM and make some attempt to present QM on an axiomatic basis. But most texts, such as Griffiths, have a more relaxed approach and never clearly state the postulates. What is your preference?

Arguments FOR:1) Distinction between axioms and

theorems is critical learning goal in any science course

2) Framework of Postulates necessary to view QM as coherent structure.

AGAINST:1) Dishonest: QM is too complex

to be axiomatized2) Pedagogically useless: does not

help students.

Present the Postulates in junior QM?

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yes slightly no

Textbooks: Postulates or Not?Most of the 20 texts examined do not state the Postulates.

Textbooks: Postulates or Not?

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Yes No

Faculty: Teach Collapse or Not?

Faculty Q: Do you teach the collapse postulate (II)?

The measurement Postulates of QM:

I. Pr(a) = |a||2 II. | |a

Teach Wavefunction Collapse?

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Yes Reluctantly No

Many faculty unhappy with collapse postulate.

"This is a pragmatic response to a deep mystery that no one understands."

"This is the price we pay for pretending that a single particle can exist in an unentangled state."

"The collapse postulate is implausible; I don't like it. But the coherent story is not there for me if you take it out of QM."

"I myself am unsure whether the collapse postulate is part of the formal structure of QM. The collapse refers to an ideal quantum measurement that cannot be realized in practice."

"This can't really be right, because we believe the universe undergoes unitary evolution. So this non-unitary [acausal] behavior must be a tentative stand-in for some deeper understanding which we hope will come when we can deal with large numbers of entangled particles. But we have to adopt this view, because it works. "

Textbooks: Collapse or Not?Half of the textbooks we examined have no mention of the Collapse Postulate.

Textbooks: Include Collapse or Not?

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None Little Complete

Information Wave or Matter Wave?

Q for faculty: How should you present the physical interpretation of the wavefunction to students?

Information Wave interpretation: the wave function is a mathematical object which provides information only about the results of measurement, that is, the interaction between the quantum system and a macroscopic measuring apparatus. In this view, it makes little or no sense to talk about what the quantum system is "doing" in the absence of measurement. The wave function does not describe the system itself, rather it describes the possible results of interactions of the system with the outside world.

Matter wave interpretation: the wave function of a quantum system describes the system itself. A matter wave proponent ascribes some kind of physical reality to the wavefunction and would have no problem saying something like "The electron went through both slits."

Faculty view of the wavefunction:Information wave or Matter Wave?

Information Wave or Matter Wave?

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Info Mixed Matter

Info Wave or Matter Wave?

"Well, the matter wave view is wrong."

"I lean toward the matter wave interpretation. I am partial to ascribing physical meaning to the wavefunction. "

Distinguished theorist A:

Distinguished theorist B:

Distinguished theorist C:"If pressed, I choose the info wave interpretation. But when I talk about the wavefunction, I talk like I believed in matter waves. In fact, I don't care, because it has no effect on the things I calculate."

Conclusions

• Growing consensus on textbook: Griffiths

• Little consensus on Teaching of postulates Teaching of collapse of wavefunction Interpretation of the wavefunction

Opportunity for addressing nature-of-science questions in the classroom.

"QM is not a finished system, I think. So it is healthy that there are diverse ways of teaching it. I think it would be a catastrophe if everyone taught it the same way. "

- David J. Griffiths.