It is not clear what is your problem, and how exactly did you connected to the reader, but there are a few things you should check...
1. Did you crossed the tx/rx lines? You should!
2. SoftwareSerial has its limitation about what port can be used as rx. Check here:
https://www.arduino.cc/en/Reference/SoftwareSerial[
^], and consider to use an Arduino board with more than one hardware serial (Mega?).
// UPDATE
#include "Arduino.h"
unsigned char incomingByte;
void sendIdentifyCmd ()
{
Serial2.write (0x40);
Serial2.write (0x04);
Serial2.write (0x01);
Serial2.write (0x01);
Serial2.write (0xCD);
}
void setup ()
{
Serial.begin (9600);
while(Serial);
Serial2.begin (9600);
while(Serial2);
Serial.println ("begin initial Serial!\n");
}
void loop ()
{
sendIdentifyCmd ();
delay (2);
while(Serial2.available() < 64)
{
incomingByte = Serial2.read();
Serial.println(incomingByte,HEX);
delay(1000);
}
Serial.println ();
delay (1000);
}