An important component of learning physics is being able to apply concepts and reasoning when solving problems. This can be especially challenging for students in quantum mechanics courses, in which the mathematical nature of the theory requires students adjust to new and unfamiliar ways of attaining "understanding". This paper describes the application of the Essential Skills Framework in an upper-division quantum mechanics course. A preliminary set of "essential skills" were proposed that underlie the solutions of common problems related to probabilities in quantum mechanics. Homework assignments were then developed that provided students with practice in applying these skills. The effect was assessed both by examining the accuracy and speed of students in using these skills over repeated homework assignments as well as through the impact on a standard course exam. Significant improvements were observed, although to a different extent on different types of questions. The results suggest that essential skills practice can be productively incorporated into courses on quantum mechanics, but certain skills are more difficult and may need special attention.