How common is Dirac notation?

[abskebabs]

I was just wondering, because we spent our entire 3rd year Quantum Mechanics course using it. One of my lecturers(evidently, not the one teaching me the module!), seemed to bear a very negative sentiment towards its relevance; I asked him if anybody still uses it in Research, and he said the last person who did had a name beginning with D and ending in C...

 

Personally, I came to appreciate the notation in the sense it provided a certain elegance and understanding of QM more broadly in terms of linear operators acting in vector spaces, as well as having to solve less cumbersome ODEs from schrodinger wave mechanics.

 

So, was he right? Is what I've been taught within a lecture course once again redundant in today's world?

[swansont]

Depends on the research. I haven't used dirac notation for my job very much at all, but I'm an experimentalist. If you look at papers, I think you'll see it's fairly common.

[ajb]

Dirac notation is widespread in physics. It is a very convenient way to describe things in a basis independent way.

 

It is in less common usage by mathematicians in analysis, but some do use it.

 

Personally, it is how I would do it but my work at the moment does not involve Hilbert spaces and similar.

[Severian]

I have noticed that some lecturers have a bad habit of using Dirac notation non-rigourously, where [math]|\psi \rangle[/math] is basically shorthand for the wavefunction and [math]\langle \psi |[/math] is its conjugate.

 

In my opinion, this is very bad, and leads to confusion among students. It is much better to define Dirac notation rigourously as a vector in Hilbert space and use relations like [math]\psi(x) = \langle x | \psi \rangle[/math] to define wavefunctions.

 

It may be that your lectures were about topics where one can simply use wavefunctions and don't need the complication of Hilbert spaces. For example, a basic QM course about particles in potential wells, or even the hydrogen atom. If so, then I am inclined to agree that Dirac notation is an unnecessary complication.

 

However, Dirac notation is very useful when doing more formal QM and also when going beyond it to study Quantum Field Theory. So it is definitely not fair to say that Dirac notation has no relevance to research.

[abskebabs]

I have noticed that some lecturers have a bad habit of using Dirac notation non-rigourously, where [math]|\psi \rangle[/math] is basically shorthand for the wavefunction and [math]\langle \psi |[/math] is its conjugate.

 

In my opinion, this is very bad, and leads to confusion among students. It is much better to define Dirac notation rigourously as a vector in Hilbert space and use relations like [math]\psi(x) = \langle x | \psi \rangle[/math] to define wavefunctions.

 

It may be that your lectures were about topics where one can simply use wavefunctions and don't need the complication of Hilbert spaces. For example, a basic QM course about particles in potential wells, or even the hydrogen atom. If so, then I am inclined to agree that Dirac notation is an unnecessary complication.

 

However, Dirac notation is very useful when doing more formal QM and also when going beyond it to study Quantum Field Theory. So it is definitely not fair to say that Dirac notation has no relevance to research.

 

Hmmm... no my lecturer actually didn't have such a non-rigorous approach and I was fully aware that [math]\psi(x)[/math] is simply the component of the state vector in the X basis, though I did use Shankar to do a lot of my revision, especially of the maths. Not sure if all my peers share the same views exactly.

 

My impressions gained from the comments so far; it seems perhaps this was just a highly opinionated statement by one of my other lecturers. I think he favoured a somewhat more abstract and general treatment.

[timo]

Just out of interest: What's that lecturer's field of research?

[abskebabs]

Just out of interest: What's that lecturer's field of research?

I'm guessing you're asking about the one who was the critic. Well, I'm studying theoretical physics and both professors in question are theorists too. I actually went to see him today about projects for my final(4th year) today, and I did get the impression he does do a lot of work on Quantum and Classical modelling

of certain magnetic magnetic materials, or at least sets a lot of projects on them! I'm sure he does do a lot more however,

 

Our theory department does seem to do a lot of condensed matter, superconductivity and cold atom work too... I couldn't help but get the impression over the last few years we're very "applied" for a theory department!