All right, sci-fi lovers, would you curl up with a Romulan ale for 60 Earth minutes with this one...
COLUMBIA (TV Sci-Fi Drama Series) A psychiatrist must confront the possibility a young woman tormented by schizophrenia is suffering from the psychological effects of faster-than-light travel.
OP, here is an invaluable resource for writing loglines:
http://www.twoadverbs.com/logline.pdf
In my opinion, your logline needs improvement from a writing standpoint, independent of what the story is about.
For one, it's not written sharply enough or concisely enough. The logline could also use more punch.
Can you think of an adjective to describe the psychiatrist?
Is he or she a world-famous psychiatrist? An alcoholic psychiatrist? A sexually frustrated psychiatrist?
Don't use meaningless adjectives, but pick something descriptive enough to give an insight into your character and the story.
Finally, what is the conflict? Is the psychiatrist skeptical of the patient's claims? I'm not sure you presented a strong enough conflict to make a great story.
My advice would be to try looking at this idea from another point of view:
COLUMBIA
After experiencing faster-than-light travel for the first time, a suddenly schizophrenic astronaut struggles to conceal her hallucinations from the rest of the crew, some of whom begin to fear for their own safety.
That may not be the route you want to go with this story, but hopefully that serves as a halfway decent example of what a logline should be.
In as few words as possible, you want to present characters and conflict, and make it sound compelling.