bringing gun in a train and in an amtrak?

Don D is not quite correct. You can declare a firearm when traveling by air in your checked luggage. There are various requirements about how they packed and locked that vary by airline, and most don't allow any ammunition, even separate from the firearm. If you plan on traveling by air with a checked firearm is is best to assure that you completely understand the particular airline's requirements.

Amtrack will soon be allowing you to check a firearm in much like an airline does. I'm not completely sure when that goes into effect.

Guns are absolutely prohibited on airplanes--carried on your person or checked through in your luggage. Even the attempt to bring one on board will subject you to immediate arrest.

The situation with Amtrak is a bit more complex. This is from their website:

The Departments of Transportation and Housing and Urban Development, and Related Agencies Appropriations Act of 2010, enacted into law on December 16, 2009, requires Amtrak to implement the procedures necessary to provide storage and carriage of firearms in checked baggage cars and at Amtrak stations that accept checked baggage, within one year of the bill’s enactment. This requirement applies solely to checked baggage, not carry-on baggage.

Amtrak’s current policy prohibits all firearms, ammunition and other weapons aboard its trains. This includes any being carried on the person, in carry-on baggage or in checked baggage. Please be advised that this policy remains in effect until Amtrak begins firearm carriage service by December 2010.

As for the gun on an airplane. Are you kidding? You can't bring a nail-file on an American airline! You can't bring liquids over three ounces(88mL) on an airplane. As for a gun on an Amtrak train, I doubt it. If you try bringing a gun into an American airport, you'll be immediately arrested. That's not a place where guns are OK.