No, you can't use WhatsApp with the same number only on mobiles. But that does not mean you can't.
WhatsApp is providing such facilities called WhatsApp Web. Simply, you have to open your browser like Google Chrome, then open https://web.whatsapp.com. There you will get the QR code. Open your WhatsApp application for once, and click on an option where you get WhatApp Web. On clicking that, it shows the QR code scanner. You only have to scan the QR code that is already opened in your browser. After scanning, it will display all the conversations, and here you can use WhatsApp from another device.
But there is a little limitation for using WhatsApp Web, that mobile having a SIM card should be connected to the internet.
