I have sleep apnea and periodic limb movement disease. Can I deduct the cost of a split matress bed so I my limb movements do not disturb my wie's sleep?

can I deduct the cost of my half of the split bed/matress

no, it has to be medically necessary.  If you needed an adjustable bed so you could sleep upright to not stop breathing then you would be able to deduct that.  But, it has to be for actual medical purposes.

No, you can only deduct the medical expense for the person who has the medical diagnosis.  A bed that benefits your wife, since she does not have a diagnosis that needs the bed, is not deductible.