Control of Matter Waves in Adjacent Potential Wells

✍ Scribed by K. Kime

• Book ID: 101289256
• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 262 KB
• Volume: 20
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(19970310)20:4<369::aid-mma870>3.0.co;2-7

✦ Synopsis

We consider exact controllability of a system of two Schro¨dinger equations. These represent matter waves in adjacent potential wells with different potentials, one zero, the other a positive constant »

. The problem is formulated as a simultaneous boundary controllability problem, with Dirichlet control. Estimates for the controls, including an observability inequality, are proved using multiplier techniques. Then the Hilbert uniqueness method is used to obtain the exact controllability result. If » is sufficiently small, there exists a time ¹ K (» ) such that the system is exactly controllable in times ¹'¹ K (» ).