I want to implement a date chooser using a JSlider. The user should be able to use the slider to freely choose between two previously known dates. I've seen examples like this one:

But I want to do the same, using only one slider. The minimal distance between two points (tick) should be one day. Any hints how to implement that?

If you want to have a slider with min = 1.1.2012 and max = 10.1.2012 just create a slider with min = 0 and max = number of days in between, then add the selected number to 1.1.2012.
I assume 10.1.2012 means January 10th, thus your slider would have min = 0 and max = 9. Then set the labels accordingly.