What does the 0-ket in this state function expression represent?

[davidge]

I would like to know what the "0-ket", called vacuum state and used in the following expression, represents $$\Psi(x,t) = \int d^3x <x| \ a^{\dagger}(x) \ |0>$$ I have rewritten the expression for the case of just one $x$. The expression above is usually presented with $(x_1,...x_n)$ (n particles), in which case we have to integrate over each $x_i$.

 

[PeterDonis]

the following expression

Where are you getting this expression from? It doesn't look right, since there is a dependence on $t$ on the LHS but nothing on the RHS has anything to do with $t$.

 

[davidge]

Where are you getting this expression from? It doesn't look right, since there is a dependence on $t$ on the LHS but nothing on the RHS has anything to do with $t$.

Sorry, it was a typo. The expression as I saw it, is find below. I have it in my QM-folder. As I got it long time ago, I will not be able to tell you where I got it from.

 

[PeterDonis]

As I got it long time ago, I will not be able to tell you where I got it from.

Sorry, without a valid reference, I have no way of responding, except to say that what's in your QM folder still doesn't look quite right (nor does it look the same, for the case of one dimension, as what you wrote in the OP). This is why we ask for references to textbooks and peer-reviewed papers directly, not something you might have gotten from it at some time but can't remember, and apparently miscopied something when you wrote it down.

Thread closed.