While I fully understand where the lack of motivation comes from I have to say that indulging it to the point where you're not working is unethical. If you were asking about refusing to do overtime (paid or unpaid) then that would be different, I don't think many people would expect an employee working out their notice to be going an extra inch, let alone an extra mile, but your question reads as referring to your normal duties. You know, that thing that they pay you for. Imagine the flip side of this question (from the employer's perspective):
An employee has resigned from the organisation, and is currently in the notice period. I don't have any interest in paying them during the notice period. Is this ethical?
They have already quit the job and have to stay here 1 more month, so is it ok not to pay them?
Anyway they're leaving, and I certainly have no interest in paying them. Also this is an employee that I didn't like working for us, from the start, just wanted to get rid somehow from the beginning.
See what I mean?
From a pragmatic point of view you have to consider that how you behave during your notice period may still affect your references and depending on your location and industry potentially your professional reputation as well. Is it really worth risking compromising any of that for sake of one month more of working there and being professional?
Remember that unless you have a lot of handover to do or projects that you are expected to complete in that time your workload will naturally tail off towards the end of that month anyway.