Unfortunately, law and science are not always on the same page. Narcotics generally refer to substances that produce a stupor associated with analgesia. This is the opposite of the effect produced by cocaine.  Although cocaine tinctures are used to numb the eye in some situtations.  

Georgia makes a distinction with regard to sentencing between narcotic and non-narcotic Schedule II drugs.  Cocaine appears in Schedule II.

Georgia defines narcotic drug as including any product, extraction, chemical synthesis, or combination of extraction and synthesis  of opium and opiates and related chemicals, opium poppy and poppy straw, coca leaves.

For those that are interested, here is the full definition:

OCGA 16-13-21 (17) “Narcotic drug” means any of the following, whether produced directly or indirectly by extraction from substances of vegetable origin, or independently by means of chemical synthesis, or by a combination of extraction and chemical synthesis:

(A) Opium and opiate, and any salt, compound, derivative, or preparation of opium or opiate;

(B) Any salt, compound, isomer, derivative, or preparation thereof which is chemically equivalent or identical to any of the substances referred to in subparagraph (A) of this paragraph, but not including the isoquinoline alkaloids of opium;

(C) Opium poppy and poppy straw; or

(D) Coca leaves and any salt, compound, derivative, stereoisomers of cocaine, or preparation of coca leaves, and any salt, compound, stereoisomers of cocaine, derivative, or preparation thereof which is chemically equivalent or identical to any of these substances, but not including decocainized coca leaves or extractions of coca leaves which do not contain cocaine or ecgonine.

You may see indictments or accusations in Georgia referring to cocaine as a narcotic drug.  It may be wrong medically, but it is correct legally, at least in Georgia. 

"When I use a word, it means just what I choose it to mean—neither more, nor less."  Lewis Carroll, Through the Looking Glass

Simple possession of a Schedule II non-narcotic drug is punished as a felony based on aggregate weight:  less than two grams carries from one to three years in prison, at least two grams but less than four grams carries one to eight years, and four grams or more but less than 28 grams carries one to fifteen years.

Simple possession of a Schedule I drug or a narcotic Schedule II drug is punished as a felony based on aggregate weight: less than one gram carries one to three years, one gram or more but less than four grams carries one to eight years, and four grams or more but less than 28 grams carries one to 15 years.